Pattern recognition is the quiet engine behind almost every intelligence test ever written. Before a question asks you to calculate anything, it asks you to notice something — a gap that keeps doubling, a letter that keeps sliding three places forward, a shape that gains one side each time. Spot the rule and the answer falls out in seconds. Miss it and no amount of arithmetic will rescue you.
That is why series questions dominate IQ tests, graduate aptitude papers, bank and civil service exams, and the reasoning rounds of technical job interviews. They are compact, culture-light and very hard to fake. They also happen to be enormously satisfying to solve, which is why number and letter series puzzles have stayed popular for well over a century.
This collection gives you 60 pattern recognition questions with full answers and worked explanations, arranged from gentle warm-ups to genuinely awkward ones. They are split into five sets: easy number series, medium number series, hard and genius-level number series, letter and alphabet series, and shape and visual pattern questions. Every answer is explained, so even the ones you miss teach you a rule you can reuse.
Grab a pen, cover the answers, and keep score as you go. There is a scoring guide further down, along with seven techniques that will crack the large majority of series questions you will ever meet. If you would like a broader warm-up first, our 100+ brain teaser IQ questions mix pattern work with lateral thinking.
What Is Pattern Recognition (And Why Tests Love It)?
Pattern recognition is the ability to detect a repeating structure in information and to predict what the structure will produce next. In a reasoning test it usually appears as a series: an ordered run of numbers, letters or shapes governed by a rule that is never stated. Your job is to reverse-engineer the rule from the evidence in front of you and apply it one step further.
Psychologists call this fluid reasoning — the capacity to solve novel problems without relying on stored knowledge. It is the reason series questions travel so well across languages and education systems. You do not need to know history or vocabulary to see that 3, 6, 12, 24 is doubling. That independence from background knowledge makes series items one of the fairest and most widely used item types in cognitive assessment.
There is a practical payoff too. Series questions reward a very specific habit: calculating the differences between consecutive terms before you do anything else. That single move solves a surprising share of them outright, and it is a habit you can build in an afternoon. If your mental arithmetic is the bottleneck rather than the pattern-spotting, our guide to simple maths tricks for everyone is worth a detour before you start.
Roughly speaking, easy items use one rule, medium items hide the rule one layer down in the differences, and hard items either combine two rules or abandon arithmetic altogether. Knowing which of those three worlds you are in is most of the battle.
Easy Number Series Questions (1–15)
These fifteen use a single, unchanging rule — add, subtract, multiply or divide by a fixed amount, or recognise a famous sequence. If you find yourself stuck on any of them, look at the gap between the first two terms and check whether that same gap holds all the way along.
1. What comes next? 2, 4, 6, 8, __
Answer: 10
A simple +2 step. Every term is even, and the gap never changes.
2. What comes next? 5, 10, 15, 20, __
Answer: 25
The five times table. Each term adds 5.
3. What comes next? 3, 6, 12, 24, __
Answer: 48
Each term doubles: ×2 every step.
4. What comes next? 100, 90, 80, 70, __
Answer: 60
A descending series with a constant step of −10.
5. What comes next? 1, 4, 9, 16, __
Answer: 25
These are perfect squares: 1², 2², 3², 4², 5².
6. What comes next? 2, 3, 5, 7, 11, __
Answer: 13
The prime numbers in order. 13 is the next number divisible only by 1 and itself.
7. What comes next? 1, 1, 2, 3, 5, 8, __
Answer: 13
The Fibonacci sequence: each term is the sum of the two before it (5 + 8 = 13).
8. What comes next? 7, 14, 21, 28, __
Answer: 35
The seven times table; the step is a constant +7.
9. What comes next? 81, 27, 9, 3, __
Answer: 1
Each term is divided by 3.
10. What comes next? 1, 8, 27, 64, __
Answer: 125
Perfect cubes: 1³, 2³, 3³, 4³, 5³.
11. What comes next? 12, 15, 18, 21, __
Answer: 24
A constant +3 step.
12. What comes next? 50, 45, 40, 35, __
Answer: 30
A constant −5 step.
13. What comes next? 2, 6, 18, 54, __
Answer: 162
Each term is multiplied by 3.
14. What comes next? 11, 22, 33, 44, __
Answer: 55
The eleven times table; a constant +11 step.
15. What comes next? 64, 32, 16, 8, __
Answer: 4
Each term is halved.
Medium Number Series Questions (16–30)
The rule is now one layer down. In most of these the differences between terms form their own sequence, so the move is to write those differences underneath and look again. A few use squares or cubes with a small adjustment, and two use a combined operation such as ×2 + 1.
16. What comes next? 3, 7, 15, 31, __
Answer: 63
The rule is ×2 + 1. Check: 31 × 2 + 1 = 63.
17. What comes next? 1, 3, 6, 10, 15, __
Answer: 21
Triangular numbers. The gaps grow +2, +3, +4, +5, +6, so 15 + 6 = 21.
18. What comes next? 2, 6, 12, 20, 30, __
Answer: 42
Each term is n × (n + 1): 1×2, 2×3, 3×4, 4×5, 5×6, 6×7 = 42.
19. What comes next? 6, 11, 21, 36, 56, __
Answer: 81
The gaps are 5, 10, 15, 20, 25. Add 25 to 56 to get 81.
20. What comes next? 1, 2, 6, 24, 120, __
Answer: 720
Factorials. Multiply by 2, then 3, then 4, then 5, then 6: 120 × 6 = 720.
21. What comes next? 8, 12, 20, 36, __
Answer: 68
The gaps double: 4, 8, 16, then 32. So 36 + 32 = 68.
22. What comes next? 3, 8, 15, 24, 35, __
Answer: 48
Each term is n² − 1: 4−1, 9−1, 16−1, 25−1, 36−1, 49−1 = 48.
23. What comes next? 120, 99, 80, 63, 48, __
Answer: 35
Again n² − 1, but counting down: 121−1, 100−1, 81−1, 64−1, 49−1, then 36−1 = 35.
24. What comes next? 2, 3, 5, 9, 17, __
Answer: 33
The gaps double: 1, 2, 4, 8, then 16. So 17 + 16 = 33.
25. What comes next? 10, 14, 23, 39, 64, __
Answer: 100
The gaps are the square numbers 4, 9, 16, 25, then 36. So 64 + 36 = 100.
26. What comes next? 7, 10, 16, 28, __
Answer: 52
The gaps double: 3, 6, 12, then 24. So 28 + 24 = 52.
27. What comes next? 1, 4, 13, 40, __
Answer: 121
The rule is ×3 + 1. Check: 40 × 3 + 1 = 121.
28. What comes next? 9, 16, 25, 36, 49, __
Answer: 64
Squares of 3, 4, 5, 6, 7, then 8² = 64.
29. What comes next? 240, 120, 40, 10, __
Answer: 2
The divisor grows each step: ÷2, ÷3, ÷4, then ÷5. So 10 ÷ 5 = 2.
30. What comes next? 5, 6, 9, 14, 21, __
Answer: 30
The gaps are the odd numbers 1, 3, 5, 7, then 9. So 21 + 9 = 30.
Hard and Genius-Level Number Series (31–42)
This is where most people slow down. Several of these combine two rules, one alternates its operation on every step, and three abandon arithmetic entirely — the answer depends on the digits themselves rather than their value. If a question here refuses to yield to differences or ratios after a minute, that is your signal to stop calculating and start reading. Solvers who enjoy this kind of misdirection will find more of it in our logical questions to test your IQ.
31. What comes next? 2, 12, 36, 80, __
Answer: 150
Each term is n³ + n²: (1+1), (8+4), (27+9), (64+16), then (125+25) = 150.
32. What comes next? 1, 5, 14, 30, 55, __
Answer: 91
Running totals of the squares: 1, 1+4, 1+4+9, 1+4+9+16, and so on. Add 6² = 36 to 55 to get 91.
33. What comes next? 3, 12, 27, 48, 75, __
Answer: 108
Each term is 3n²: 3×1, 3×4, 3×9, 3×16, 3×25, then 3×36 = 108.
34. What comes next? 0, 7, 26, 63, 124, __
Answer: 215
Each term is n³ − 1: 1−1, 8−1, 27−1, 64−1, 125−1, then 216−1 = 215.
35. What comes next? 2, 5, 10, 17, 26, __
Answer: 37
Each term is n² + 1: 1+1, 4+1, 9+1, 16+1, 25+1, then 36+1 = 37.
36. What comes next? 5, 25, 61, 113, __
Answer: 181
The gaps are 20, 36, 52 — each 16 more than the last. The next gap is 68, so 113 + 68 = 181.
37. What comes next? 6, 24, 60, 120, 210, __
Answer: 336
Each term is n(n+1)(n+2): 1×2×3, 2×3×4, 3×4×5, 4×5×6, 5×6×7, then 6×7×8 = 336.
38. What comes next? 13, 35, 57, 79, __
Answer: 911
Forget arithmetic — read the digits. Each term is a pair of consecutive odd numbers stuck together: 1|3, 3|5, 5|7, 7|9, then 9|11 = 911.
39. What comes next? 1, 11, 21, 1211, 111221, __
Answer: 312211
This is the “look and say” sequence: you describe the previous term out loud. 111221 is three 1s, two 2s, one 1 — written as 312211.
40. What comes next? 4, 7, 15, 29, 59, __
Answer: 117
The rule alternates: ×2 − 1, then ×2 + 1. Since 29 × 2 + 1 = 59, the next step is 59 × 2 − 1 = 117.
41. What comes next? 11, 13, 17, 19, 23, 29, __
Answer: 31
Prime numbers again, but starting mid-sequence. After 29 the next prime is 31 (note that 25 and 27 are skipped).
42. What comes next? 1, 3, 11, 43, __
Answer: 171
The rule is ×4 − 1. Check: 43 × 4 − 1 = 171.
Letter and Alphabet Series Questions (43–52)
Letter series work exactly like number series once you convert each letter to its alphabet position: A is 1, Z is 26. The only extra difficulty is the conversion itself, which is why writing the positions above the letters is almost always worth the five seconds it costs. Watch for groups where two letters follow different rules at the same time.
43. What comes next? A, C, E, G, __
Answer: I
Skip one letter each time: A, (B), C, (D), E, (F), G, (H), I.
44. What comes next? B, D, F, H, __
Answer: J
The even-positioned letters of the alphabet, stepping +2.
45. What comes next? Z, X, V, T, __
Answer: R
Running backwards and skipping one letter: 26, 24, 22, 20, then 18 = R.
46. What comes next? A, D, G, J, __
Answer: M
Step +3 in alphabet position: 1, 4, 7, 10, then 13 = M.
47. What comes next? AZ, BY, CX, DW, __
Answer: EV
Two rules at once. The first letter moves forward (A, B, C, D, E) while the second moves backward (Z, Y, X, W, V).
48. What comes next? ACE, BDF, CEG, __
Answer: DFH
Every letter in the group shifts forward by one: C→D, E→F, G→H.
49. What comes next? Z, Y, X, W, V, __
Answer: U
The alphabet in reverse, one letter at a time.
50. What comes next? A, B, D, G, K, __
Answer: P
The gaps grow: +1, +2, +3, +4, then +5. K is position 11, so 11 + 5 = 16 = P.
51. What comes next? JAN, MAR, MAY, JUL, __
Answer: SEP
Month abbreviations, skipping every other month: January, March, May, July, September.
52. What comes next? CMG, EOI, GQK, __
Answer: ISM
Each of the three letters steps forward by 2: C→E→G→I, M→O→Q→S, G→I→K→M.
Shape and Visual Pattern Questions (53–60)
Spatial items test the same rule-finding instinct applied to position, rotation and count. Each of these is described in words so you can solve it without a diagram — sketch the figure on paper if it helps, because drawing the second and third steps yourself is often what makes the rule visible.
53. A sequence shows a triangle, then a square, then a pentagon, then a hexagon. What shape comes next?
Answer: A heptagon (7 sides)
The rule is the side count: 3, 4, 5, 6, then 7.
54. A square has a single dot in its top-left corner. The square is rotated 90° clockwise at each step. Where is the dot after 4 steps?
Answer: Back in the top-left corner
Four 90° turns make a full 360° rotation, so the dot returns to where it started.
55. Triangular arrangements of dots contain 1, 3, 6 and 10 dots. How many dots are in the next arrangement?
Answer: 15
Each new row adds one more dot than the last: +2, +3, +4, then +5. So 10 + 5 = 15.
56. A growing figure is drawn with 3, 5, 7 and 9 line segments. How many segments does the next figure use?
Answer: 11
A constant +2 each step.
57. A row of dots doubles at every step: 1 dot, 2 dots, 4 dots, 8 dots. How many at the next step?
Answer: 16
Each step multiplies the count by 2.
58. A single clock hand starts pointing at 12 and turns 60° clockwise at each step. Which hour mark does it point to after 5 steps?
Answer: 10
Five turns of 60° is 300° clockwise. Each hour mark is 30°, so 300 ÷ 30 = 10 hour marks round from 12.
59. A square is split into four quadrants, and one shaded quadrant moves one position clockwise at each step. Starting top-left, which quadrant is shaded after 7 steps?
Answer: Bottom-left
The cycle repeats every 4 steps, and 7 ÷ 4 leaves a remainder of 3. Three clockwise moves from top-left gives top-right, bottom-right, bottom-left.
60. Matchsticks form a row of joined squares: 1 square uses 4 sticks, 2 squares use 7, 3 squares use 10. How many sticks for 10 squares?
Answer: 31
The first square costs 4 sticks and every extra square costs 3 more. So 4 + (9 × 3) = 31.
How Did You Do? A Scoring Guide
Give yourself one point for every correct answer out of 60. The explanation does not have to match ours word for word — several of these series can be described in more than one valid way, and what matters is that your rule reproduces the same next term.
One caveat worth stating plainly: this is a practice set, not a validated IQ test. A real psychometric score comes from a standardised, timed instrument administered under controlled conditions and compared against a normed sample. Treat your score here as feedback on one specific skill, not as a measurement of general intelligence. If you want to see how the same reasoning gets tested in a hiring context, our IQ questions to ace your next interview covers the formats recruiters actually use.
7 Techniques for Cracking Almost Any Series Question
Technique one does most of the work. In a typical aptitude paper, writing the differences under the series solves or half-solves the majority of number items, and it takes about four seconds. Technique seven is the one people skip under time pressure, and it is where most avoidable marks are lost.
The same discipline transfers directly to verbal items, where the “rule” is a relationship between words rather than numbers — our round-up of verbal reasoning interview questions shows how that looks in practice.
Four Mistakes That Cost People Marks
There is a fifth, subtler one: assuming every series has a single correct answer. Mathematically, any finite run of numbers can be continued by infinitely many rules. What test writers mean by “correct” is the simplest rule that fits every term given. When you are torn between two candidate rules, pick the one that needs fewer moving parts.
Summary
Pattern recognition questions look like maths problems but behave like observation problems. The arithmetic in a series item is almost always trivial — adding 36, multiplying by three, subtracting one from a square. What separates a score of 25 from a score of 55 is not calculation speed but the discipline of looking in the right place first.
Across these 60 questions, three moves carried most of the solutions. Writing the differences underneath the series exposed the rule in the easy and medium sets. Recognising the squares and cubes on sight handled most of the hard set. And being willing to abandon arithmetic entirely — reading digits, letters or shapes as symbols rather than quantities — unlocked the handful of genius-level items that defeat people who keep looking for a sum.
If you worked through the whole set, you now have a usable mental library: constant steps, constant ratios, growing gaps, powers, two-step rules and digit tricks. That library is what makes an experienced test-taker look fast. They are not calculating more quickly than you; they are recognising a shape they have already seen and skipping straight to the answer.
Come back in a week and try the hard set again cold. Recall after a gap is a far better measure of whether a pattern has really stuck than getting it right the first time with the explanation sitting just below.
Frequently Asked Questions
Can a number series question have more than one correct answer?
Strictly speaking, yes. Any finite sequence can be continued by infinitely many valid formulas. In practice, test writers intend the simplest rule that accounts for every term given, and that rule is almost always unambiguous once you check it across the whole series rather than just the last two terms.
What is the fastest way to solve a number series?
Write the differences between consecutive terms underneath the series before trying anything else. If the differences are constant, you have the answer. If they form their own recognisable pattern, apply the same trick to them. If they are chaotic, switch to ratios, then to squares and cubes, then to two-step rules.
Do pattern recognition questions really measure intelligence?
They measure fluid reasoning, which is one well-studied component of general intelligence and correlates reasonably with overall cognitive test performance. They do not measure knowledge, creativity, judgement or practical skill, and a practice set like this one is not a validated psychometric instrument.
Can you get better at series questions by practising?
Yes, substantially — though what improves is mostly familiarity rather than raw reasoning capacity. Once you have seen fifty series, you recognise the common rule families instantly instead of deriving them, which is why practised candidates finish these sections so much faster.
Which exams use number and letter series questions?
They appear in graduate aptitude tests, banking and civil service exams, armed forces entrance tests, many technical job screenings, and standard IQ batteries. Letter series in particular are a staple of clerical and administrative aptitude papers.
How long should each question take?
On a timed paper, budget roughly 30 to 45 seconds for an easy or medium item and up to 90 seconds for a hard one. If a question passes two minutes with no rule in sight, flag it and move on — the marks lost by running out of time exceed those lost by skipping one awkward item.
Related Articles
- 100+ Brain Teaser IQ Questions and Answers — the broadest set on the site, mixing pattern work with lateral thinking and wordplay. The natural next stop after this page.
- 50 Best IQ Test Questions with Answers — a shorter, test-style run covering numerical, verbal and spatial items in the proportions a real battery uses.
- 20+ Logical Questions and Answers to Test Your IQ — deduction and inference puzzles where the rule is stated but the conclusion is hidden, the mirror image of series work.
- 100 Riddles for Adults With Answers — easy through to lateral and maths riddles, for when you want the answer to make you laugh rather than nod.
- 75 Brain Teasers for Kids With Answers — the same reasoning skills pitched for younger solvers, sorted into easy, medium and hard.
- Simple Math Tricks For Everyone — mental arithmetic shortcuts that make the calculation half of a series question effectively free.
- Top IQ Questions to Ace Your Next Interview — how reasoning questions are actually used in hiring, and what interviewers are listening for in your explanation.
- Best Trivia Questions and Answers for Team Building — a lighter format for groups, if you want to run these as a session rather than solo.
