Reasoning · 18 min read

Series

Series questions are pure pattern recognition under a clock, which makes them the most trainable topic in the paper. There is no theory to learn — only a fixed order of checks that you run until something fits, and enough familiarity with squares, cubes and the alphabet that the fit is obvious rather than discovered.

One organisational note before you start. In banking papers, number series lives in the quantitative section while alphanumeric series lives in reasoning; in SSC and railway papers both sit under general intelligence. They are the same skill, so this page treats them together.

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Current affairs · 19 September 2026

Today’s current affairs, checked at the source

Every item is dated, read on the conducting body’s or ministry’s own site, and written with the question it becomes. Read today’s items, take the quiz, or download the month as a PDF.

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19September 2026

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What to note today

  1. 01

    No charges on UPI payments up to ₹2,000 and on RuPay debit cards, by notification

    Economy and banking14 SeptemberMinistry of Finance notification of 14 September 2026

  2. 02

    Retail inflation rose to 4.82 per cent in August 2026

    Economy and banking14 SeptemberMoSPI CPI press release of 14 September 2026

  3. 03

    SEMICON India 2026 opened at Yashobhoomi on the theme “Silicon to Systems”

    Science and technology17–19 SeptemberPrime Minister’s Office note of 16 September 2026; inauguration confirmed by agreeing reports of 17 September

  4. 04

Why it matters

Series in the exam

Direct question counts move between cycles, so treat these as ranges rather than promises. Check the notification for the pattern you are sitting.
ExamExpected questionsHow it usually appears
SSC CGL / CHSL Tier 12–5 questionsMissing-number and alphanumeric series, plus a separate number series in the quant section.
Banking Prelims (IBPS / SBI)3–5 questionsAlphanumeric series in reasoning; number and wrong-number series in the quant section.
Banking Mains3–5 questionsWrong-number series and harder two-level patterns.
RRB NTPC / Group D3–4 questionsStraight number and alphabet series — among the fastest marks in the paper.
CTET / Teaching exams1–2 questionsSimple arithmetic and letter series.

Start here

The order of checks

Do not stare at a series looking for inspiration. Run this list in order — it takes about twenty seconds end to end and it catches almost every pattern an exam uses.

Run these in order

  • 1. Write the differences underneathAlways the first move, without exception. If the differences are constant you are done in five seconds; if not, you now have a second series to look at.
  • 2. Take the differences of those differencesA constant second difference means the pattern is quadratic — the differences themselves form an arithmetic series, as in 2, 5, 11, 20, 32 where the gaps run 3, 6, 9, 12.
  • 3. Check the ratiosDivide each term by the previous one. A constant ratio is a geometric series; a ratio that creeps up — roughly 2, then 2.2, then 2.1 — suggests "multiply and add".
  • 4. Compare against squares and cubesIf a term is near 121, 144, 169 or near 125, 216, 343, test n² or n³ with a small offset. This is why the tables further down are worth memorising.
  • 5. Try alternate termsRead the 1st, 3rd and 5th terms as one series and the 2nd, 4th and 6th as another. Two interleaved series look like nonsense until you split them.

The length of the series tells you something

A series of four or five terms is almost always a simple rule — differences, ratios or powers. A series of seven or eight terms is usually two interleaved series, because the examiner needs enough terms for each half to be recognisable. Count the terms before you start and you will know which check to run first.

The catalogue

Number series types

Every number series in an Indian competitive exam is one of these, or two of them interleaved. Read the examples until the shapes are familiar rather than memorising the names.

The patterns examiners actually use
TypeExampleHow to spot it
Arithmetic5, 10, 15, 20, 25Constant difference. The differences row is flat.
Geometric3, 6, 12, 24, 48Constant ratio. Each term divides cleanly into the next.
Multiply and add3, 7, 15, 31, 63Each term is ×2 + 1. Ratios hover just under the multiplier.
Increasing multiplier2, 4, 12, 48, 240Multiplied by 2, then 3, then 4, then 5.
Increasing operator5, 11, 24, 51, 106Each term is ×2 and then +1, +2, +3, +4 in turn.
Square-based2, 5, 10, 17, 26Each term is n² + 1 for n = 1, 2, 3, 4, 5.
Cube-based9, 28, 65, 126Each term is n³ + 1 for n = 2, 3, 4, 5.
Product of consecutives2, 6, 12, 20, 30, 42Each term is n(n + 1). Differences rise by two each time.
Power series1, 4, 27, 256, 3125Each term is n to its own power: 1¹, 2², 3³, 4⁴, 5⁵.
Fibonacci-type2, 3, 5, 8, 13, 21Each term is the sum of the previous two.
Prime-based2, 3, 5, 7, 11, 13Or primes with an offset, such as 4, 5, 7, 9, 13.
Alternating1, 4, 3, 9, 5, 16, 7Odd positions form one series, even positions another.

Two rules can produce the same first three terms

The sequence 3, 7, 15 fits "×2 + 1" and also fits "add 4, add 8, add 16". They agree all the way to 63 and would only diverge later. That is fine — when two rules agree on every term you are given, either one produces the correct answer. What is not fine is testing a rule on two terms and applying it to the fourth.

Where the harder questions live

Two-level and mixed patterns

When the differences are not constant, they are usually a series in their own right. That is the whole of the "difficult" half of this topic.

Find the next term: 2, 5, 11, 20, 32, ?

  1. Differences: 3, 6, 9, 12.
  2. Those differences are themselves arithmetic, rising by 3 each time.
  3. The next difference is 15.
  4. 32 + 15.

Answer: 47.

Find the next term: 5, 11, 24, 51, ?

  1. Differences are 6, 13, 27 — not obviously patterned, so check ratios instead: roughly 2.2, 2.18, 2.13.
  2. Close to 2, so test "multiply by 2 and add something": 5 × 2 + 1 = 11, and 11 × 2 + 2 = 24.
  3. Confirm on the next: 24 × 2 + 3 = 51. The added number climbs by one each step.
  4. 51 × 2 + 4.

Answer: 106.

Alternating series
Split the terms by position. In 1, 4, 3, 9, 5, 16, 7, the odd positions run 1, 3, 5, 7 and the even positions run 4, 9, 16 — that is 2², 3², 4², so the next even-position term is 25.
Difference series that is geometric
In 3, 7, 15, 31, 63 the differences are 4, 8, 16, 32 — doubling. This is the same series as "×2 + 1", seen from the other side.
Series with a division step
Some series shrink: 720, 120, 24, 6, 2 divides by 6, then 5, then 4, then 3. Whenever terms fall, check divisors before anything else.
Series built on a moving operator
Terms such as +2, ×2, +4, ×4 alternate two operations. Suspect this when the differences alternate between small and large.

Banking favourite

Wrong number series

A complete series is given with one term replaced by an incorrect one, and you must name the intruder. The method is the same as before, with one extra habit.

How to find the odd term out

  • Establish the pattern from the first three termsThey are almost never the wrong one — examiners plant the error in the middle or near the end so that a candidate reading forwards commits to the right rule first.
  • Then walk forwards and stop at the first breakThe first term that fails the rule is the answer, provided every later term fits once you resume from the corrected value.
  • If two terms seem to break, your rule is wrongExactly one term is incorrect. Two failures means you fitted a pattern to the wrong pair of terms — go back and re-derive it.
  • State what the term should have beenIt is the cheapest possible check. If you cannot name the correct replacement, you have not really found the pattern.

Find the wrong number: 8, 27, 64, 125, 216, 343, 500

  1. The first terms are 2³, 3³ and 4³, so the rule is consecutive cubes.
  2. Continuing: 5³ = 125 and 6³ = 216 and 7³ = 343 all fit.
  3. The next should be 8³ = 512.

Answer: 500 is wrong; it should be 512.

Find the wrong number: 5, 10, 17, 26, 37, 50, 64

  1. Differences: 5, 7, 9, 11, 13, 14 — the last one breaks a clean odd-number run.
  2. Check against squares: 5 = 2² + 1, 10 = 3² + 1, 17 = 4² + 1, 26 = 5² + 1, 37 = 6² + 1, 50 = 7² + 1.
  3. So the last term should be 8² + 1.

Answer: 64 is wrong; it should be 65.

Number series in disguise

Letter and alphabet series

Convert every letter to its alphabet position and you are back to a number series. That single move solves the entire type.

The conversions you need

  • Write the position under each letter before you look for anythingA, C, F, J, O becomes 1, 3, 6, 10, 15 — and the differences 2, 3, 4, 5 are then unmissable.
  • EJOTY: E = 5, J = 10, O = 15, T = 20, Y = 25Anchors that let you convert in either direction without counting from A.
  • Paired letters usually move in opposite directionsIn AZ, BY, CX, DW the first letters climb and the second letters fall — and each pair sums to 27.
  • Wrap past Z back to AA gap that runs off the end of the alphabet continues from the beginning, exactly as in coding-decoding.
  • Watch for a repeated-letter blockSeries such as AB, DE, GH, JK move in blocks of three positions; convert the first letter of each block and treat the rest as decoration.

Find the next term: A, C, F, J, O, ?

  1. Positions: 1, 3, 6, 10, 15.
  2. Differences: 2, 3, 4, 5 — rising by one.
  3. The next gap is 6, so the position is 15 + 6 = 21.
  4. The 21st letter is U.

Answer: U.

Pure banking reasoning

Alphanumeric series

A single line mixing letters, digits and symbols is given, followed by four or five counting questions. There is no pattern to find — the whole skill is careful reading, and that is precisely why candidates lose marks here.

How to work the block

  • Number every position before reading any questionWrite 1, 2, 3 … under the elements. Every question then becomes arithmetic on those numbers instead of finger-counting across the line.
  • "nth to the right of the mth from the left" is position m + n from the leftThe fifth to the right of the seventh from the left is position 12. The same works mirrored from the right end.
  • "Immediately preceded by" means the element just before itPreceded looks left, followed looks right. Reversing these two words is the most common single error in the topic.
  • Handle "how many X are preceded by Y and followed by Z" as a scanGo along the line once, testing each X against both conditions. Do not try to hold the answer in your head — tally it in the margin.
  • First and last elements can never satisfy both conditionsThe first has nothing before it and the last nothing after it, so cross them out at the start of any two-sided condition.

In the sequence 4 P $ 7 B 2 % K 9 M # 5 R A 3, how many digits are immediately preceded by a letter and immediately followed by a symbol?

  1. Number the positions 1 to 15. The digits sit at positions 1, 4, 6, 9, 12 and 15.
  2. Position 1 has nothing before it and position 15 nothing after it, so both are out.
  3. Position 4 is preceded by the symbol $, so it fails. Position 12 is preceded by the symbol #, so it fails.
  4. Position 9 is preceded by K but followed by M, a letter, so it fails.
  5. Position 6 is preceded by B and followed by %, satisfying both conditions.

Answer: One — the digit 2.

These are the fastest marks in a banking reasoning paper

An alphanumeric block of five questions can be finished in ninety seconds once the positions are numbered, against roughly four minutes for a puzzle set worth the same five marks. If you take nothing else from this page into the exam hall, take the habit of attempting this block first.

Recall, not reasoning

The numbers worth memorising

Recognising 361 as 19² instantly is the difference between a ten-second question and a ninety-second one. There is no shortcut for this — it is recall.

Squares, cubes and primes to have on instant recall
RangeWhat to knowWhy it matters
Squares 1–30… 121, 144, 169, 196, 225, 256, 289, 324, 361, 400 …Square-based series stay under 900 in almost every paper.
Cubes 1–151, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331 …Cube series are common and the gaps grow fast, so recognition is everything.
Primes under 502, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47Prime series and prime-with-offset series appear in SSC papers.
Factorials to 61, 2, 6, 24, 120, 720A falling series that divides by 6, 5, 4, 3 is a factorial read backwards.
Powers of 2 and 32, 4, 8, 16, 32, 64, 128 · 3, 9, 27, 81, 243Geometric series almost always use one of these two bases.

Error log

Where marks are lost

Series is a topic where the wrong answers are cheap to avoid, because almost all of them come from the same three habits.

Testing a rule on two terms
Any two numbers fit some rule. Confirm on at least three consecutive terms — including the last one given — before you compute the answer.
Not writing the differences down
Candidates try to hold the difference row in their heads to save four seconds, and then lose forty reconstructing it. Write it under the series every single time.
Spending more than a minute
If no pattern has appeared in sixty seconds, mark the question and move on. Series questions are all worth the same, and the next one is often trivial.
Confusing "preceded" and "followed"
In alphanumeric blocks this single confusion can cost four of the five marks in the set, because the same misreading applies to every question in it. Underline the two words in the first question you read.
Answering the wrong end of the series
Some questions ask for the missing middle term, not the next one. Check which position the question mark occupies before you compute anything.

Solved examples

Worked line by line

Read the steps rather than the answer. The method is what transfers to the next question.

Find the next term: 3, 7, 15, 31, 63, ?

  1. Differences: 4, 8, 16, 32 — doubling.
  2. The next difference is 64.
  3. Equivalently, each term is the previous one × 2 + 1, and 63 × 2 + 1 gives the same result.

Answer: 127.

Find the next term: 2, 5, 11, 20, 32, ?

  1. Differences: 3, 6, 9, 12 — arithmetic, rising by 3.
  2. The next difference is 15.
  3. 32 + 15.

Answer: 47.

Find the next term: 5, 11, 24, 51, ?

  1. Ratios sit just above 2, so test "×2 and add".
  2. 5 × 2 + 1 = 11, 11 × 2 + 2 = 24, 24 × 2 + 3 = 51. The addend climbs by one.
  3. 51 × 2 + 4.

Answer: 106.

Find the next term: 1, 4, 27, 256, ?

  1. 1 = 1¹, 4 = 2², 27 = 3³, 256 = 4⁴.
  2. Each term is n raised to its own power.
  3. The next is 5⁵.

Answer: 3125.

Find the missing term: 2, 6, 12, 20, 30, ?, 56

  1. Differences: 4, 6, 8, 10 — rising by two.
  2. The next difference is 12, giving 42, and the one after that is 14, giving 56 — which matches the last given term.
  3. Equivalently each term is n(n + 1): 1×2, 2×3, 3×4, 4×5, 5×6, 6×7, 7×8.

Answer: 42.

Find the wrong number: 8, 27, 64, 125, 216, 343, 500

  1. The opening terms are 2³, 3³ and 4³.
  2. 125, 216 and 343 continue the cubes correctly.
  3. The eighth cube is 512.

Answer: 500 is wrong; it should be 512.

Find the wrong number: 5, 10, 17, 26, 37, 50, 64

  1. Differences are 5, 7, 9, 11, 13 and then 14, which breaks the run of odd numbers.
  2. Test against squares: each term is n² + 1 for n = 2, 3, 4, 5, 6, 7.
  3. The next should be 8² + 1.

Answer: 64 is wrong; it should be 65.

Find the next term: A, C, F, J, O, ?

  1. Positions: 1, 3, 6, 10, 15.
  2. Differences: 2, 3, 4, 5.
  3. The next gap is 6, giving position 21.

Answer: U.

Find the next term: AZ, BY, CX, DW, ?

  1. First letters: A, B, C, D — climbing by one, so the next is E.
  2. Second letters: Z, Y, X, W — falling by one, so the next is V.
  3. Each pair also sums to 27, which confirms it: E is 5 and V is 22.

Answer: EV.

In the sequence 4 P $ 7 B 2 % K 9 M # 5 R A 3, how many digits are immediately preceded by a letter and immediately followed by a symbol?

  1. Number the fifteen positions. Digits sit at 1, 4, 6, 9, 12 and 15.
  2. Positions 1 and 15 are at the ends, so neither can meet a two-sided condition.
  3. Positions 4 and 12 are preceded by symbols, and position 9 is followed by a letter.
  4. Position 6 has B before it and % after it.

Answer: One.

Practice

16 questions on Series

Work each one out before you reveal the answer — the explanation is where the marks are.

  1. Q1Find the next term: 3, 7, 15, 31, 63, ?

    • A125
    • B127
    • C129
    • D121

  2. Q2Find the next term: 2, 5, 11, 20, 32, ?

    • A47
    • B44
    • C45
    • D49

  3. Q3Find the next term: 5, 11, 24, 51, ?

    • A104
    • B105
    • C106
    • D108

  4. Q4Find the next term: 1, 4, 27, 256, ?

    • A3125
    • B625
    • C1024
    • D3025

  5. Q5Find the next term: 3, 6, 12, 24, ?

    • A36
    • B42
    • C30
    • D48

  6. Q6Find the missing term: 2, 6, 12, 20, 30, ?, 56

    • A40
    • B42
    • C44
    • D46

  7. Q7Find the wrong number: 8, 27, 64, 125, 216, 343, 500

    • A216
    • B343
    • C125
    • D500

  8. Q8Find the wrong number: 4, 9, 19, 39, 79, 160

    • A19
    • B39
    • C79
    • D160

  9. Q9Find the wrong number: 5, 10, 17, 26, 37, 50, 64

    • A37
    • B50
    • C26
    • D64

  10. Q10Find the next term: A, C, F, J, O, ?

    • AT
    • BU
    • CV
    • DS

  11. Q11Find the next term: AZ, BY, CX, DW, ?

    • AEV
    • BFU
    • CEU
    • DFV

  12. Q12Find the next term: B, D, G, K, ?

    • AN
    • BO
    • CP
    • DQ

  13. Q13Find the next term: 1, 4, 3, 9, 5, 16, 7, ?

    • A9
    • B36
    • C21
    • D25

  14. Q14Find the next term: 2, 3, 5, 8, 13, ?

    • A18
    • B20
    • C21
    • D22

  15. Q15In the sequence 4 P $ 7 B 2 % K 9 M # 5 R A 3, how many digits are immediately preceded by a letter and immediately followed by a symbol?

    • ANone
    • BOne
    • CTwo
    • DThree

  16. Q16In that same sequence, which element is fifth to the right of the seventh from the left end?

    • AM
    • B#
    • C5
    • DR

Questions

Series — FAQs

How do I solve number series questions quickly?

Run a fixed order of checks rather than searching for inspiration. Write the differences underneath; if they are not constant, take their differences; then check the ratios; then compare terms against squares and cubes; and finally try reading alternate terms as two separate series. The whole routine takes about twenty seconds.

What are the main types of number series?

Arithmetic and geometric series, multiply-and-add patterns, series with an increasing multiplier or addend, square- and cube-based series, products of consecutive numbers, power series such as 1¹, 2², 3³, Fibonacci-type sums, prime-based series and alternating series where odd and even positions follow different rules.

How do I find the wrong number in a series?

Establish the pattern from the first three terms — the error is almost always planted later — then walk forwards and stop at the first term that breaks it. If two terms seem to break the rule, your rule is wrong rather than the series, because exactly one term is incorrect. Always name what the term should have been as a check.

How do I solve letter and alphabet series?

Write the alphabet position under each letter and the problem becomes an ordinary number series. A, C, F, J, O turns into 1, 3, 6, 10, 15, and the differences 2, 3, 4, 5 make the next term obvious. Use the EJOTY anchors to convert quickly in both directions.

What is alphanumeric series in bank exams?

A single line of letters, digits and symbols, followed by four or five counting questions — how many digits are preceded by a letter, which element is fifth to the right of the seventh from the left, and so on. There is no pattern to discover; the skill is numbering the positions first and reading the conditions exactly.

What does "nth to the right of the mth from the left" mean?

Simply position m + n from the left. The fifth to the right of the seventh from the left is position 12. The mirrored phrase works the same way from the right end, so convert it into a single position number and stop counting on your fingers.

What is the difference between "preceded by" and "followed by"?

Preceded by refers to the element immediately before, and followed by to the element immediately after. Reversing them is the most expensive error in alphanumeric series, because the same misreading usually applies to every question in the block.

Which numbers should I memorise for series questions?

Squares to 30, cubes to 15, primes under 50, factorials to 720 and the powers of 2 and 3. Recognising 361 as 19² or 343 as 7³ instantly is what turns a ninety-second question into a ten-second one.

How much time should a series question take?

Thirty to forty seconds for a straightforward one and up to a minute for a two-level pattern. If nothing has appeared after sixty seconds, mark it and move on — every series question carries the same marks and the next one is often trivial.

Is number series part of reasoning or quantitative aptitude?

It depends on the exam. In banking papers, number series sits in the quantitative section while alphanumeric series sits in reasoning. In SSC and railway papers both appear under general intelligence and reasoning. The skill is identical either way.

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