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Number and Letter Series

CSAT · Logical Reasoning

Introduction

Series questions ask for the next or missing term. Most CSAT series follow a handful of patterns; checking them in a fixed order solves nearly every question in under a minute.

Key concepts

Patterns to test, in order

  1. Constant difference (arithmetic): 7, 12, 17, 22 → +5.
  2. Changing difference: differences 2, 4, 6, 8 or 1, 4, 9, 16.
  3. Multiplication / division: 3, 6, 12, 24 (×2); ×2 + 1 patterns: 2, 5, 11, 23.
  4. Squares and cubes: 4, 9, 16, 25; 8, 27, 64; squares ± 1: 3, 8, 15, 24.
  5. Alternating series: two series interleaved: 2, 20, 4, 18, 6, 16.
  6. Sum of previous terms: 1, 2, 3, 5, 8 (Fibonacci-type).
  7. Primes: 2, 3, 5, 7, 11, 13.

Letter series

Convert letters to positions and treat them as numbers: C, F, I, L → 3, 6, 9, 12 (+3). Pairs like AZ, BY, CX use opposite letters. Groups (ABC, DEF, GHI) may have patterns across positions.

Wrong-term questions

Find the pattern using most of the terms, then the one that breaks it is the odd term.

A checking routine for any series

  1. Write the differences between consecutive terms. If they are constant, the series is arithmetic.
  2. If the differences themselves form a pattern (constant, doubling, squares), use second differences.
  3. If the differences grow quickly, test ratios: ×2, ×3, or alternating ×2 +1.
  4. Look for squares and cubes (1, 4, 9, 16 … ; 1, 8, 27, 64 …) or squares ± 1.
  5. Split odd and even positions – two interleaved series are common.
  6. For letters, convert to positions (A = 1 … Z = 26) and apply the same tests; remember EJOTY for 5, 10, 15, 20, 25.

Wrong-term questions

When asked to find the term that does not fit, fix the pattern from the majority of terms and check each term against it. The odd term usually breaks only one difference, which then makes the next difference look wrong too – so check both neighbours before choosing.

Time management

Series questions are quick marks when the pattern is simple and time sinks when it is not. Give each one about a minute; if no pattern appears after testing differences, ratios and alternation, mark it and move on.

📐 Formula box
  • Squares 1–30 and cubes 1–15 by heart
  • nth term of AP = a + (n − 1)d
  • Opposite letters: positions add to 27

Solved examples

Example 1

Find the next term: G, J, M, P, S, ?

(a) V (b) W (c) X (d) U

✅ Worked solution
  1. Pattern: each letter moves 3 places forward (skip 2).
  2. Next = V.

Answer: (a) V

Example 2

Find the next term: I, M, Q, U, Y, ?

(a) B (b) C (c) E (d) D

✅ Worked solution
  1. Pattern: each letter moves 4 places forward (skip 3).
  2. Next = C.

Answer: (b) C

Example 3

Find the next term: D, G, J, M, P, ?

(a) U (b) R (c) T (d) S

✅ Worked solution
  1. Pattern: each letter moves 3 places forward (skip 2).
  2. Next = S.

Answer: (d) S

Example 4

Find the next number in the series: 2, 3, 5, 8, 13, ?

(a) 22 (b) 26 (c) 21 (d) 19

✅ Worked solution
  1. Pattern: each term is the sum of the previous two.
  2. Next term = 21.

Answer: (c) 21

Example 5

Find the next number in the series: 26, 37, 50, 65, 82, ?

(a) 118 (b) 101 (c) 102 (d) 99

✅ Worked solution
  1. Pattern: squares of 5, 6, … plus 1.
  2. Next term = 101.

Answer: (b) 101

Example 6

Find the next term: DW, FU, HS, JQ, LO, ?

(a) NM (b) OM (c) MM (d) MN

✅ Worked solution
  1. Pattern: first letters move +2; second letters are their opposites (moving −2).
  2. Next = NM.

Answer: (a) NM

Example 7

Find the next term: HS, MN, RI, WD, BY, ?

(a) TG (b) FT (c) GT (d) HT

✅ Worked solution
  1. Pattern: first letters move +5; second letters are their opposites (moving −5).
  2. Next = GT.

Answer: (c) GT

Example 8

Find the next number in the series: 3, 5, 8, 13, 21, ?

(a) 42 (b) 32 (c) 35 (d) 34

✅ Worked solution
  1. Pattern: each term is the sum of the previous two.
  2. Next term = 34.

Answer: (d) 34

Example 9

Find the next number in the series: 4, 7, 10, 13, 16, ?

(a) 22 (b) 19 (c) 17 (d) 20

✅ Worked solution
  1. Pattern: add 3 each time.
  2. Next term = 19.

Answer: (b) 19

Example 10

Find the next term: D, H, L, P, T, ?

(a) X (b) W (c) Y (d) Z

✅ Worked solution
  1. Pattern: each letter moves 4 places forward (skip 3).
  2. Next = X.

Answer: (a) X

💡 Shortcut / exam tip
  • Always write the first differences; if they are irregular, write the second differences or ratios.
  • Big jumps suggest multiplication or powers; small changes suggest addition.
  • In letter series, write positions under each letter.
⚠️ Common traps
  • Stopping at the first pattern that fits three terms – check all given terms.
  • Forgetting alternate-term series.
  • Off-by-one when wrapping past Z.

Practice set

Attempt all 12 questions (about 90 seconds each), then check the worked solutions below.

Q1. Find the next number in the series: 49, 64, 81, 100, 121, ?

(a) 144 (b) 165 (c) 142 (d) 145

Q2. Find the next term: I, K, M, O, Q, ?

(a) T (b) U (c) R (d) S

Q3. Find the next number in the series: 7, 9, 12, 16, 21, ?

(a) 25 (b) 28 (c) 32 (d) 27

Q4. Find the next term: IR, NM, SH, XC, CX, ?

(a) SH (b) IS (c) GS (d) HS

Q5. Find the next term: D, F, H, J, L, ?

(a) M (b) N (c) O (d) P

Q6. Find the next term: E, J, O, T, Y, ?

(a) C (b) D (c) E (d) F

Q7. Find the next term: A, F, K, P, U, ?

(a) B (b) Y (c) Z (d) A

Q8. Find the next number in the series: 9, 16, 25, 36, 49, ?

(a) 65 (b) 64 (c) 62 (d) 77

Q9. Find the next number in the series: 5, 15, 45, 135, 405, ?

(a) 1216 (b) 1213 (c) 1215 (d) 1485

Q10. Find the next number in the series: 2, 4, 8, 16, 32, ?

(a) 62 (b) 65 (c) 64 (d) 80

Q11. Find the next number in the series: 2, 8, 14, 20, 26, ?

(a) 32 (b) 30 (c) 33 (d) 38

Q12. Find the next term: I, L, O, R, U, ?

(a) X (b) Z (c) Y (d) W

✅ Answers and worked solutions

Q1 – (a) 144. Pattern: squares of 7, 8, …. Next term = 144.

Q2 – (d) S. Pattern: each letter moves 2 places forward (skip 1). Next = S.

Q3 – (d) 27. Pattern: differences increase by 1: 2, 3, 4, 5, 6. Next term = 27.

Q4 – (d) HS. Pattern: first letters move +5; second letters are their opposites (moving −5). Next = HS.

Q5 – (b) N. Pattern: each letter moves 2 places forward (skip 1). Next = N.

Q6 – (b) D. Pattern: each letter moves 5 places forward (skip 4). Next = D.

Q7 – (c) Z. Pattern: each letter moves 5 places forward (skip 4). Next = Z.

Q8 – (b) 64. Pattern: squares of 3, 4, …. Next term = 64.

Q9 – (c) 1215. Pattern: multiply by 3 each time. Next term = 1215.

Q10 – (c) 64. Pattern: multiply by 2 each time. Next term = 64.

Q11 – (a) 32. Pattern: add 6 each time. Next term = 32.

Q12 – (a) X. Pattern: each letter moves 3 places forward (skip 2). Next = X.

⚡ Quick revision
  • Difference → second difference → ratio
  • Squares/cubes ± k
  • Alternating series
  • Letters → numbers

Revision note

One-page note / PDF
  • Difference → second difference → ratio
  • Squares/cubes ± k
  • Alternating series
  • Letters → numbers
Revision card summarising Number and Letter Series
One-page visual summary of the key points to revise.
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