{"id":37900,"date":"2026-04-08T15:14:29","date_gmt":"2026-04-08T08:14:29","guid":{"rendered":"https:\/\/times.edu.vn\/?p=37900"},"modified":"2026-05-08T16:46:04","modified_gmt":"2026-05-08T09:46:04","slug":"igcse-sequences-questions","status":"publish","type":"post","link":"https:\/\/times.edu.vn\/en\/igcse\/igcse-sequences-questions\/","title":{"rendered":"IGCSE Maths Sequences Questions: Linear, Quadratic &#038; Geometric for A*"},"content":{"rendered":"<p><strong><a href=\"https:\/\/times.edu.vn\/en\/igcse\/what-is-igcse-a-comprehensive-guide-for-students\/\">IGCSE<\/a><\/strong><strong>\u00a0<\/strong><strong>sequences<\/strong><strong>\u00a0questions<\/strong> test whether you can recognize number patterns quickly and turn them into correct rules, especially the <strong>nth term<\/strong>.<\/p>\n<p>High-scoring answers classify the sequence first (Arithmetic Progression with a <strong>common difference<\/strong>, <strong>geometric sequence<\/strong>\u00a0with a common ratio, or <strong>quadratic nth term<\/strong>\u00a0using <strong>second differences<\/strong>) and then prove the rule with a short check.<\/p>\n<p>You\u2019re expected to continue sequences, find an nth-term formula for any position, and handle harder pattern-recognition cases like alternating, Fibonacci-type, or diagrammatic sequences.<\/p>\n<p>The most reliable exam tactic is to use difference\/ratio tests, write the right template, and substitute cleanly for large terms.<\/p>\n<h2><strong>IGCSE sequences questions: <\/strong><strong>A<\/strong><strong>\u00a0high-score strategy guide from Times Edu<\/strong><\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-37941\" src=\"https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/04\/7-10.webp\" alt=\"IGCSE Sequences Questions 2026: How to Spot Patterns and Answer with More Confidence\" width=\"1000\" height=\"558\" srcset=\"https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/04\/7-10.webp 1000w, https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/04\/7-10-300x167.webp 300w, https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/04\/7-10-768x429.webp 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/p>\n<p>IGCSE sequences\u00a0questions look simple, but they are engineered to test pattern recognition, algebraic reasoning, and exam discipline under time pressure.<\/p>\n<p>The best students do not \u201cguess the pattern\u201d; they classify the sequence quickly, write the correct structure, and then prove it with checks.<\/p>\n<p>Based on our years of practical tutoring at Times Edu, the fastest improvement comes when students stop treating sequences as isolated tricks and start treating them as a decision tree: <strong>L<\/strong><strong>inear (Arithmetic Progression)<\/strong>, <strong>geometric (Geometric Sequence)<\/strong>, <strong>quadratic (Quadratic nth term)<\/strong>, or \u201cnon-standard\u201d (cubic, Fibonacci-type, diagrammatic).<\/p>\n<p><strong style=\"color: #f00;\">&gt;&gt;&gt; Read more:<\/strong> <a class=\"xem-them-link\" href=\"https:\/\/times.edu.vn\/en\/ib\/igcse-to-ib-skills\/\">IGCSE to IB Skills<\/a> 2026: What Study Habits and Academic Skills Students Need to Succeed<\/p>\n<h2><strong>Finding the nth term for IGCSE sequences questions<\/strong><\/h2>\n<p>The core skill in IGCSE sequences\u00a0questions is moving from \u201cterm-to-term thinking\u201d to \u201cposition-to-term thinking.\u201d Examiners reward students who can produce an explicit <strong>nth Term<\/strong>\u00a0formula and then use it to compute large positions like the 50th term without writing 49 steps.<\/p>\n<h3><strong>Term-to-term vs position-to-term (do not confuse these)<\/strong><\/h3>\n<p>Term-to-term rules describe how you get from one term to the next (add 3, multiply by 2, alternate). Position-to-term rules give a direct formula in terms of <strong>n<\/strong>, the term number.<\/p>\n<p>A critical detail most students overlook in the 2026 exam cycle is that many 2\u20133 mark questions are designed to trap students who only describe the pattern in words. The mark scheme typically requires an algebraic expression (your <strong>nth Term<\/strong>), plus a quick check.<\/p>\n<h3><strong>Linear sequences: Arithmetic Progression and common difference<\/strong><\/h3>\n<p>A linear sequence is an <strong>Arithmetic Progression<\/strong>. The difference between consecutive terms is constant: The <strong>Common Difference<\/strong>.<\/p>\n<p><strong>Method (fast and exam-safe):<\/strong><\/p>\n<ul>\n<li>Find the common difference: D=T2\u2212T1d=T2\u200b\u2212T1\u200b<\/li>\n<li>Use the structure: Nth Term=a+(n\u22121)dnth Term=a+(n\u22121)d<\/li>\n<li>Simplify to a form like kn+ckn+c<\/li>\n<\/ul>\n<p><strong>Example:<\/strong>\u00a02,5,8,11,\u20262,5,8,11,\u2026<\/p>\n<ul>\n<li>Common difference d=3d=3. First term a=2a=2.<\/li>\n<\/ul>\n<p>Tn=2+(n\u22121)\u22c53=3n\u22121Tn\u200b=2+(n\u22121)\u22c53=3n\u22121<\/p>\n<p>Check: N=1\u21d22n=1\u21d22, n=2\u21d25n=2\u21d25. Done.<\/p>\n<p><strong>Common misconception:<\/strong>\u00a0Students write 2+3n2+3n. That gives 55 when n=1n=1, which fails instantly.<\/p>\n<h3><strong>A comparison table you should memorise<\/strong><\/h3>\n<table>\n<tbody>\n<tr>\n<th colspan=\"1\" rowspan=\"1\"><strong>Sequence type (what it <\/strong><strong>is<\/strong><strong>)<\/strong><\/th>\n<th colspan=\"1\" rowspan=\"1\"><strong>Quick test<\/strong><\/th>\n<th colspan=\"1\" rowspan=\"1\"><strong>Key keyword(s)<\/strong><\/th>\n<th colspan=\"1\" rowspan=\"1\"><strong>nth Term template<\/strong><\/th>\n<th colspan=\"1\" rowspan=\"1\"><strong>Typical trap<\/strong><\/th>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">Arithmetic Progression (linear)<\/td>\n<td colspan=\"1\" rowspan=\"1\">First differences constant<\/td>\n<td colspan=\"1\" rowspan=\"1\">Common Difference, nth Term<\/td>\n<td colspan=\"1\" rowspan=\"1\">a+(n\u22121)da+(n\u22121)d<\/td>\n<td colspan=\"1\" rowspan=\"1\">Using a+nda+nd<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">Geometric Sequence<\/td>\n<td colspan=\"1\" rowspan=\"1\">Ratios constant<\/td>\n<td colspan=\"1\" rowspan=\"1\">Common Ratio<\/td>\n<td colspan=\"1\" rowspan=\"1\">arn\u22121arn\u22121<\/td>\n<td colspan=\"1\" rowspan=\"1\">Using difference instead of ratio<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">Quadratic sequence<\/td>\n<td colspan=\"1\" rowspan=\"1\">Second Difference constant<\/td>\n<td colspan=\"1\" rowspan=\"1\">Second Difference, Quadratic nth term<\/td>\n<td colspan=\"1\" rowspan=\"1\">an2+bn+can2+bn+c<\/td>\n<td colspan=\"1\" rowspan=\"1\">Forgetting second differences<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">Cubic \/ higher<\/td>\n<td colspan=\"1\" rowspan=\"1\">Third differences constant<\/td>\n<td colspan=\"1\" rowspan=\"1\">Pattern Recognition<\/td>\n<td colspan=\"1\" rowspan=\"1\">an3+bn2+cn+dan3+bn2+cn+d<\/td>\n<td colspan=\"1\" rowspan=\"1\">Treating as quadratic<\/td>\n<\/tr>\n<tr>\n<td colspan=\"1\" rowspan=\"1\">Fibonacci-type \/ recursive<\/td>\n<td colspan=\"1\" rowspan=\"1\">Depends on previous terms<\/td>\n<td colspan=\"1\" rowspan=\"1\">Pattern Recognition<\/td>\n<td colspan=\"1\" rowspan=\"1\">recursion, not closed-form<\/td>\n<td colspan=\"1\" rowspan=\"1\">Trying to force an+ban+b<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><strong>When the question asks: \u201cFind the 50th term\u201d<\/strong><\/h3>\n<p>Do not extend the sequence manually. That is a time sink and increases error probability.<\/p>\n<p><strong>Workflow:<\/strong><\/p>\n<ul>\n<li>Find nth Term expression first.<\/li>\n<li>Substitute n=50n=50.<\/li>\n<li>Show substitution cleanly, because method marks are often awarded even if arithmetic slips.<\/li>\n<\/ul>\n<p><strong style=\"color: #f00;\">&gt;&gt;&gt; Read more:<\/strong> <a class=\"xem-them-link\" href=\"https:\/\/times.edu.vn\/en\/igcse\/switching-igcse-boards\/\">Switching IGCSE Boards<\/a> 2026: A Step-by-Step Guide for Students and Parents<\/p>\n<h2><strong>Identifying linear and quadratic sequences in exam papers<\/strong><\/h2>\n<p>Most IGCSE sequences\u00a0questions are either linear or quadratic. The distinction is mechanical if you use differences properly.<\/p>\n<h3><strong>Step 1: <\/strong><strong>C<\/strong><strong>ompute first differences<\/strong><\/h3>\n<p>Subtract consecutive terms.<\/p>\n<h3><strong>Step 2: <\/strong><strong>C<\/strong><strong>heck second differences<\/strong><\/h3>\n<p>If first differences are not constant, compute the differences of the differences. If <strong>Second Difference<\/strong>\u00a0is constant, it is a quadratic sequence.<\/p>\n<p><strong>Example:<\/strong>\u00a01,4,9,16,25,\u20261,4,9,16,25,\u2026<\/p>\n<ul>\n<li>First differences: 3,5,7,93,5,7,9 (not constant)<\/li>\n<li>Second differences: 2,2,22,2,2 (constant)<\/li>\n<li>So it fits a <strong>Quadratic nth term<\/strong>.<\/li>\n<\/ul>\n<h3><strong>A reliable way to build the quadratic nth term<\/strong><\/h3>\n<p>Use the model:<\/p>\n<p>Tn=an2+bn+cTn\u200b=an2+bn+c<\/p>\n<p>For a quadratic sequence, the constant second difference equals 2a2a. So if the second difference is 2, then 2a=2\u21d2a=12a=2\u21d2a=1.<\/p>\n<p>Now plug in values:<\/p>\n<ul>\n<li>T1=a+b+cT1\u200b=a+b+c<\/li>\n<li>T2=4a+2b+cT2\u200b=4a+2b+c<\/li>\n<li>T3=9a+3b+cT3\u200b=9a+3b+c<\/li>\n<\/ul>\n<p>Solve quickly.<\/p>\n<p><strong>Example continued:<\/strong>\u00a0Tn=n2Tn\u200b=n2 appears immediately, but in exam settings you should still show the logic. Examiners reward structure, not intuition.<\/p>\n<h3><strong>Shortcut for many IGCSE quadratic patterns<\/strong><\/h3>\n<p>From our direct experience with international school curricula, the most common quadratic sequences are built from:<\/p>\n<ul>\n<li>Perfect squares (n2n2)<\/li>\n<li>Triangular numbers (n(n+1)22n(n+1)\u200b)<\/li>\n<li>\u201cSquare plus\/minus linear\u201d (n2\u00b1nn2\u00b1n, n2\u00b11n2\u00b11)<\/li>\n<\/ul>\n<p>Students who recognise these families reduce the workload dramatically, but you still need a check at n=1n=1 and n=2n=2.<\/p>\n<h3><strong>Misconceptions that cost marks in quadratic sequences<\/strong><\/h3>\n<p><strong>Mistake 1:<\/strong>\u00a0Assuming non-constant first differences means \u201cgeometric.\u201d<\/p>\n<ul>\n<li>It does not. Always check second differences first.<\/li>\n<\/ul>\n<p><strong>Mistake 2:<\/strong>\u00a0Writing an expression that fits only the first two terms.<\/p>\n<ul>\n<li>A quadratic needs at least three points to verify; use n=1,2,3n=1,2,3 checks.<\/li>\n<\/ul>\n<p><strong>Mistake 3:<\/strong>\u00a0Forgetting that second difference relates to 2a2a.<\/p>\n<ul>\n<li>This is the fastest route to aa.<\/li>\n<\/ul>\n<h3><strong>Grade-boundary reality: <\/strong><strong>W<\/strong><strong>hy sequences are \u201chigh leverage\u201d<\/strong><\/h3>\n<p>Sequences\u00a0questions are typically short and mark-dense. Students drop marks due to algebra slips, not concept gaps. That is why in many years a small cluster of topic errors can be the difference between grade boundaries.<\/p>\n<p>The pedagogical approach we recommend for high-achievers is to treat sequences as a \u201cguaranteed marks unit\u201d: Drill classification, drill nth Term construction, and drill checking. This is one of the most cost-effective topics to push a student up a grade.<\/p>\n<p><strong style=\"color: #f00;\">&gt;&gt;&gt; Read more:<\/strong> <a class=\"xem-them-link\" href=\"https:\/\/times.edu.vn\/en\/igcse\/igcse-exam-day-checklist\/\">IGCSE Exam Day<\/a> 2026 Checklist: What to Bring and Do for a Smooth Exam Experience<\/p>\n<h2><strong>Solving geometric progressions and common ratio problems<\/strong><\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-37943\" src=\"https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/04\/8-11.webp\" alt=\"IGCSE Sequences Questions 2026: How to Spot Patterns and Answer with More Confidence\" width=\"1000\" height=\"558\" srcset=\"https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/04\/8-11.webp 1000w, https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/04\/8-11-300x167.webp 300w, https:\/\/times.edu.vn\/wp-content\/uploads\/2026\/04\/8-11-768x429.webp 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/p>\n<p>A <strong>Geometric Sequence<\/strong>\u00a0multiplies by a constant ratio rr. This is not optional: If the ratio is not constant, do not call it geometric.<\/p>\n<h3><strong>How to identify a geometric sequence quickly<\/strong><\/h3>\n<p>Compute:<\/p>\n<p>R=T2T1r=T1\u200bT2\u200b\u200b<\/p>\n<p>Then verify:<\/p>\n<p>T3T2=rT2\u200bT3\u200b\u200b=r<\/p>\n<p><strong>Example:<\/strong>\u00a03,6,12,24,\u20263,6,12,24,\u2026<\/p>\n<ul>\n<li>Ratios: 2,2,22,2,2. So r=2r=2.<\/li>\n<\/ul>\n<h3><strong>The geometric nth term<\/strong><\/h3>\n<p>Tn=arn\u22121Tn\u200b=arn\u22121<\/p>\n<p>Where aa is the first term.<\/p>\n<p><strong>Example:<\/strong>\u00a0A=3,r=2a=3,r=2<\/p>\n<p>Tn=3\u22c52n\u22121Tn\u200b=3\u22c52n\u22121<\/p>\n<h3><strong>Common ratio problems with fractions and negatives<\/strong><\/h3>\n<p>These appear simple but are common mark-losers.<\/p>\n<p><strong>Fractions example:<\/strong>\u00a012,14,18,\u202621\u200b,41\u200b,81\u200b,\u2026<\/p>\n<p>R=1\/41\/2=12r=1\/21\/4\u200b=21\u200b<\/p>\n<p>So:<\/p>\n<p>Tn=12(12)n\u22121=(12)nTn\u200b=21\u200b(21\u200b)n\u22121=(21\u200b)n<\/p>\n<p><strong>Negative ratio example:<\/strong>\u00a04,\u22128,16,\u221232,\u20264,\u22128,16,\u221232,\u2026<\/p>\n<p>Here r=\u22122r=\u22122.<\/p>\n<p>Tn=4(\u22122)n\u22121Tn\u200b=4(\u22122)n\u22121<\/p>\n<p><strong>Common misconception:<\/strong>\u00a0Students treat alternating sign as \u201ctwo sequences,\u201d then lose time. It is often just a negative common ratio.<\/p>\n<h3><strong>Solving for an unknown term in a geometric sequence<\/strong><\/h3>\n<p>If you\u2019re asked to find xx in 2,x,18,\u20262,x,18,\u2026, use the ratio relationship:<\/p>\n<p>X2=18x\u21d2x2=36\u21d2x=6 or \u221262x\u200b=x18\u200b\u21d2x2=36\u21d2x=6 or \u22126<\/p>\n<p>Then check which sign is consistent with the sequence context.<\/p>\n<p><strong style=\"color: #f00;\">&gt;&gt;&gt; Read more:<\/strong> <a class=\"xem-them-link\" href=\"https:\/\/times.edu.vn\/en\/igcse\/igcse-motivation-and-study-consistency\/\">IGCSE Motivation and Study Consistency<\/a> 2026: How to Stay Focused and Revise Regularly<\/p>\n<h2><strong>Techniques for working with cubic and fibonacci-type sequences<\/strong><\/h2>\n<p>Not every IGCSE sequences\u00a0question is cleanly linear\/quadratic\/geometric. Some are designed to test adaptability and <strong>pattern recognition<\/strong>.<\/p>\n<h3><strong>Cubic sequences: <\/strong><strong>W<\/strong><strong>hen third differences are constant<\/strong><\/h3>\n<p>If first differences and second differences are not constant, compute third differences. Constant third differences indicate a cubic model:<\/p>\n<p>Tn=an3+bn2+cn+dTn\u200b=an3+bn2+cn+d<\/p>\n<p><strong>Practical exam strategy:<\/strong><\/p>\n<ul>\n<li>If a question is only 1\u20132 marks and looks messy, it may not\u00a0require a full cubic formula.<\/li>\n<li>Often they only want the next term by continuing the difference table.<\/li>\n<\/ul>\n<p><strong>Difference-table method for next term:<\/strong><\/p>\n<ul>\n<li>Build first differences, second differences, third differences.<\/li>\n<li>Extend the constant difference line by repeating it.<\/li>\n<li>Work upward to get the next term.<\/li>\n<\/ul>\n<p>This method is fast and avoids heavy algebra.<\/p>\n<h3><strong>Fibonacci-type sequences: <\/strong><strong>R<\/strong><strong>ecursive, not closed-form<\/strong><\/h3>\n<p>A Fibonacci-type sequence uses previous terms:<\/p>\n<p>Tn=Tn\u22121+Tn\u22122Tn\u200b=Tn\u22121\u200b+Tn\u22122\u200b<\/p>\n<p>Or a variant (add, subtract, multiply). IGCSE may include these as pattern continuation tasks, or as \u201cwrite a rule\u201d tasks.<\/p>\n<p><strong>Key tactic: <\/strong><strong>S<\/strong><strong>tate the recursion precisely<\/strong><\/p>\n<ul>\n<li>Do not attempt to force an nth Term like an+ban+b. That is a conceptual mismatch.<\/li>\n<\/ul>\n<p><strong>Example:<\/strong>\u00a01,1,2,3,5,8,\u20261,1,2,3,5,8,\u2026<\/p>\n<p>A correct rule:<\/p>\n<ul>\n<li>T1=1,T2=1T1\u200b=1,T2\u200b=1<\/li>\n<li>Tn=Tn\u22121+Tn\u22122Tn\u200b=Tn\u22121\u200b+Tn\u22122\u200b for n\u22653n\u22653<\/li>\n<\/ul>\n<h3><strong>Alternating and interleaved sequences<\/strong><\/h3>\n<p>If the pattern changes every other term (odd positions follow one pattern, even positions follow another), split it:<\/p>\n<p>Example: 2,5,4,7,6,9,\u20262,5,4,7,6,9,\u2026<\/p>\n<ul>\n<li>Odd positions: 2,4,6,\u20262,4,6,\u2026 (Arithmetic Progression, 2n2n)<\/li>\n<li>Even positions: 5,7,9,\u20265,7,9,\u2026 (Arithmetic Progression, 2n+32n+3 when nn counts evens)<\/li>\n<\/ul>\n<p>This is advanced <strong>Pattern Recognition<\/strong>, and it shows up in higher-difficulty IGCSE sequences\u00a0questions.<\/p>\n<p><strong style=\"color: #f00;\">&gt;&gt;&gt; Read more:<\/strong> <a class=\"xem-them-link\" href=\"https:\/\/times.edu.vn\/en\/igcse\/parents-help-with-igcse-revision\/\">Parents&amp;#8217; Help with IGCSE Revision in<\/a> 2026: Practical Support That Really Makes a Difference<\/p>\n<h2><strong>Connecting sequences to real-world patterns and modeling<\/strong><\/h2>\n<p>From our direct experience with international school curricula, exam boards like contexts that push students to model patterns rather than only compute numbers. That includes diagrammatic sequences (tiles, matchsticks, dots) and growth patterns.<\/p>\n<h3><strong>Diagrammatic sequences: <\/strong><strong>T<\/strong><strong>he marks are in the structure<\/strong><\/h3>\n<p>In visual patterns, students often count incorrectly because they do not define variables.<\/p>\n<p><strong>A clean modeling workflow:<\/strong><\/p>\n<ul>\n<li>Define what \u201cterm nn\u201d represents in the diagram.<\/li>\n<li>Count a fixed \u201ccore\u201d plus repeated \u201cunits.\u201d<\/li>\n<li>Write a formula in terms of nn, then check with n=1n=1 and n=2n=2.<\/li>\n<\/ul>\n<h3><strong>Typical structures examiners use<\/strong><\/h3>\n<ul>\n<li>Linear growth: Add a constant number of sticks\/dots each step \u2192 Arithmetic Progression model<\/li>\n<li>Quadratic growth: \u201clayers\u201d expanding around a center, squares\/rectangles increasing area \u2192 Quadratic nth term model<\/li>\n<li>Exponential growth: Repeated doubling\/halving \u2192 Geometric Sequence model<\/li>\n<\/ul>\n<h3><strong>How sequences connect to subject choices and academic planning<\/strong><\/h3>\n<p>Parents often underestimate how early maths performance influences options later. A strong IGCSE Maths profile supports smoother transitions into <a href=\"https:\/\/times.edu.vn\/en\/ib\/the-ultimate-ib-diploma-program-ibdp-guide\/\">IB<\/a>\u00a0AA HL, <a href=\"https:\/\/times.edu.vn\/en\/a-level\/what-is-a-level\/\">A-Level<\/a>\u00a0Maths\/Further Maths, and <a href=\"https:\/\/times.edu.vn\/en\/ap\/what-are-ap-course\/\">AP<\/a>\u00a0Calculus pathways.<\/p>\n<p>Based on our years of practical tutoring at Times Edu, students who master algebraic modeling early:<\/p>\n<ul>\n<li>Make fewer errors in functions, graphs, and calculus later,<\/li>\n<li>Present stronger academic consistency for competitive university applications,<\/li>\n<li>Can choose more ambitious subject combinations without risking grade drops.<\/li>\n<\/ul>\n<p>If a student is aiming for selective universities, the question is not \u201cCan they pass sequences?\u201d The question is \u201cCan they turn sequences into guaranteed marks while saving time for harder topics?\u201d<\/p>\n<p><strong style=\"color: #f00;\">&gt;&gt;&gt; Read more:<\/strong> <a class=\"xem-them-link\" href=\"https:\/\/times.edu.vn\/en\/igcse\/igcse-coursework-subjects\/\">IGCSE Coursework Subjects<\/a> 2026: Which Subjects Include Coursework and How to Prepare Well<\/p>\n<h2><strong>Frequently Asked Questions<\/strong><\/h2>\n<div class=\"hoi-dap-thok-new low-faq\">\n<div class=\"thong-tin-dai\">\n<p class=\"tit-dai\"><strong>How do you find the nth term of a quadratic sequence?<\/strong><\/p>\n<div class=\"chi-tiet-thong-tin\">Use <strong>Second Difference<\/strong>\u00a0to confirm it is quadratic. Then set Tn=an2+bn+cTn\u200b=an2+bn+c, where 2a2a equals the constant second difference. Substitute n=1,2,3n=1,2,3 to solve for bb and cc, and verify by checking if your formula reproduces the given terms.<\/div>\n<\/div>\n<div class=\"thong-tin-dai\">\n<p class=\"tit-dai\"><strong>What is the formula for a linear sequence in IGCSE?<\/strong><\/p>\n<div class=\"chi-tiet-thong-tin\">\n<p>A linear sequence is an <strong>Arithmetic Progression<\/strong>\u00a0with a constant <strong>Common Difference<\/strong>\u00a0dd. The standard form is:Tn=a+(n\u22121)dTn\u200b=a+(n\u22121)d<\/p>\n<p>It can also be simplified into kn+ckn+c after expansion.<\/p>\n<\/div>\n<\/div>\n<div class=\"thong-tin-dai\">\n<p class=\"tit-dai\"><strong>How to identify a geometric sequence in a test?<\/strong><\/p>\n<div class=\"chi-tiet-thong-tin\">Compute ratios of consecutive terms. If T2T1=T3T2T1\u200bT2\u200b\u200b=T2\u200bT3\u200b\u200b (a constant <strong>common ratio<\/strong>), it is a <strong>Geometric Sequence<\/strong>. If ratios change, it is not geometric, even if the numbers \u201clook\u201d exponential.<\/div>\n<\/div>\n<div class=\"thong-tin-dai\">\n<p class=\"tit-dai\"><strong>Are there cubic sequences in the IGCSE syllabus?<\/strong><\/p>\n<div class=\"chi-tiet-thong-tin\">Cubic-style patterns can appear in IGCSE sequences questions, especially as difference-table continuations for \u201cfind the next term.\u201d You identify them by constant third differences, but many exam questions do not require deriving a full cubic nth Term.<\/div>\n<\/div>\n<div class=\"thong-tin-dai\">\n<p class=\"tit-dai\"><strong>What is the common difference in an arithmetic progression?<\/strong><\/p>\n<div class=\"chi-tiet-thong-tin\">\n<p>The <strong>Common Difference<\/strong>\u00a0is the constant amount added (or subtracted) between consecutive terms:D=Tn+1\u2212Tnd=Tn+1\u200b\u2212Tn\u200b<\/p>\n<p>If the difference is not constant, it is not an Arithmetic Progression.<\/p>\n<\/div>\n<\/div>\n<div class=\"thong-tin-dai\">\n<p class=\"tit-dai\"><strong>How do you solve sequences involving fractions?<\/strong><\/p>\n<div class=\"chi-tiet-thong-tin\">Treat fractions exactly and test structure carefully. For arithmetic sequences, subtract terms to check constant difference (often a fraction). For geometric sequences, divide terms to check a constant ratio. Avoid decimal approximations because they create rounding errors and can hide the true pattern.<\/div>\n<\/div>\n<div class=\"thong-tin-dai\">\n<p class=\"tit-dai\"><strong>What are the hardest sequence questions in IGCSE Maths?<\/strong><\/p>\n<div class=\"chi-tiet-thong-tin\">The hardest IGCSE sequences questions typically combine multiple ideas: Alternating rules, diagrammatic modeling, \u201cfind the nth Term\u201d for a quadratic with an offset, or problems asking whether a number is in the sequence. They are hard because they punish weak <strong>pattern recognition<\/strong>\u00a0and incomplete checking, not because the algebra is advanced.<\/div>\n<\/div>\n<\/div>\n<h4>Conclusion<\/h4>\n<p>A critical detail most students overlook in the 2026 exam cycle is that you can gain marks even when your final expression is imperfect, if your method is structured and checkable. Sequences reward clean working, correct templates, and quick verification.<\/p>\n<p><strong>A high-yield weekly routine (30\u201340 minutes, 3 times\/week):<\/strong><\/p>\n<ul>\n<li>10 Minutes: Classify mixed <strong>IGCSE sequences questions<\/strong>\u00a0(linear \/ geometric \/ quadratic \/ other)<\/li>\n<li>15 Minutes: Derive <strong>nth Term<\/strong>\u00a0expressions with full checks<\/li>\n<li>10 Minutes: Mixed problem set (fractions, negative ratios, unknown term)<\/li>\n<li>5 Minutes: Error log (write the misconception and the correct trigger)<\/li>\n<\/ul>\n<p>If you want this turned into a personalised roadmap, <a href=\"https:\/\/times.edu.vn\/en\/\">Times Edu<\/a>\u00a0can map your current level to a target grade, select the exact subskills you\u2019re missing (Arithmetic Progression fluency, Geometric Sequence ratio control, Quadratic nth term construction, Second Difference recognition), and align it with your broader academic plan for IB\/A-Level\/AP readiness and university applications.<\/p>\n<p>If you share your most recent mock score, target grade, and exam board variant, we can recommend the fastest sequence-training pathway for your timeline.<\/p>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-right kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;right&quot;,&quot;id&quot;:&quot;37900&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;1&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;5&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;\u0110\u00e1nh gi\u00e1 b\u00e0i vi\u1ebft&quot;,&quot;legend&quot;:&quot;5\\\/5 - (1 vote)&quot;,&quot;size&quot;:&quot;24&quot;,&quot;title&quot;:&quot;IGCSE Maths Sequences Questions: Linear, Quadratic \\u0026amp; Geometric for A*&quot;,&quot;width&quot;:&quot;142.5&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} - ({count} {votes})&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 142.5px;\">\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-right: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 24px; height: 24px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 19.2px;\">\n            5\/5 - (1 vote)    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p>IGCSE\u00a0sequences\u00a0questions test whether you can recognize number patterns quickly and turn them into correct rules, especially the nth term. High-scoring answers classify the sequence first (Arithmetic Progression with a common difference, geometric sequence\u00a0with a common ratio, or quadratic nth term\u00a0using second differences) and then prove the rule with a short check. You\u2019re expected to continue &#8230; <a title=\"IGCSE Maths Sequences Questions: Linear, Quadratic &#038; Geometric for A*\" class=\"read-more\" href=\"https:\/\/times.edu.vn\/en\/igcse\/igcse-sequences-questions\/\" aria-label=\"Read more about IGCSE Maths Sequences Questions: Linear, Quadratic &#038; Geometric for A*\">Read more<\/a><\/p>\n","protected":false},"author":7,"featured_media":37911,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"content-type":"","rank_math_title":"","rank_math_description":"IGCSE Maths sequences questions: linear (nth term), quadratic, geometric. 5-step framework + worked examples. Paper 4 Extended A* strategy with mark scheme insights.","footnotes":""},"categories":[166],"tags":[],"class_list":["post-37900","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-igcse"],"_links":{"self":[{"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/posts\/37900","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/comments?post=37900"}],"version-history":[{"count":4,"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/posts\/37900\/revisions"}],"predecessor-version":[{"id":39629,"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/posts\/37900\/revisions\/39629"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/media\/37911"}],"wp:attachment":[{"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/media?parent=37900"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/categories?post=37900"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/times.edu.vn\/en\/wp-json\/wp\/v2\/tags?post=37900"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}