SERIES – Reasoning Notes (CUET | CLAT | IPMAT)
SERIES – Reasoning Notes (CUET | CLAT | IPMAT)
Series questions test your ability to identify patterns,
relationships, and logical progression among numbers, letters or
figures.
1. NUMBER SERIES
Type 1: Pure Addition / Subtraction Series
Concept:
Numbers change by adding or subtracting a constant value.
Example (CUET):
Q1. 7, 12, 17, 22, 27, ?
Solution:
Differences = +5, +5, +5, +5
Next = 27 + 5 = 32
Type 2: Progressive Difference Series
Concept:
Differences themselves form a pattern (constant or
arithmetic growth).
Example (IPMAT):
Q2. 3, 8, 15, 24, 35, ?
Solution:
Differences = 5, 7, 9, 11 → increasing by +2
Next difference = 13
Next term = 35 + 13 = 48
Type 3: Multiplication / Division Series
Concept:
Each term obtained by × or ÷ a constant.
Example:
Q3. 2, 6, 18, 54, ?
Solution: ×3 each step → Next = 54 × 3 = 162
Type 4: Mixed Operations (+/– with ×/÷)
Concept:
A combination of multiplication and addition/subtraction.
Example (CUET):
Q4. 5, 12, 25, 52, 105, ?
Solution:
5×2+2 = 12
12×2+1 = 25
25×2+2 = 52
52×2+1 = 105
Pattern: ×2 + (2,1,2,1…)
Next = 105×2+2 = 212
Type 5: Square / Cube Based Series
Concept:
Terms related to n², n³ or combinations.
Example:
Q5. 1, 4, 9, 16, 25, ?
Squares of 1,2,3,4,5 → next = 6² = 36
Type 6: Alternating Pattern Series
Concept:
Two separate series interwoven.
Example (CLAT):
Q6. 4, 9, 6, 11, 8, 13, ?
Odd positions: 4, 6, 8 → +2
Even positions: 9, 11, 13 → +2
Next term is even-position +2 = 15
Type 7: Prime Number Series
Concept:
Series involving prime numbers.
Example:
Q7. 2, 3, 5, 7, 11, 13, ?
Next prime = 17
Type 8: Fibonacci / Hybrid Fibonacci
Concept:
Next term = Sum of previous two (or modified form)
Example:
Q8. 3, 5, 8, 13, 21, ?
Next = 13 + 21 = 34
2. ALPHABET SERIES
Type 1: Position-Based (+n / –n)
Concept:
Use alphabet positions (A=1 to Z=26).
Example (CUET):
Q9. B, E, H, K, ?
Positions: 2, 5, 8, 11 → +3
Next = 11 + 3 = 14 → N
Type 2: Alternate Letter Pattern
Example:
Q10. A, C, F, J, O, ?
Position differences: +2, +3, +4, +5
Next difference = +6
O (15) + 6 = 21 → U
Type 3: Reverse Alphabet Series
Example (CLAT):
Q11. Z, X, V, T, ?
Positions: 26, 24, 22, 20 → –2
Next = 18 → R
Type 4: Mixed Letter & Number Transformation
Example:
Q12. A2, C4, F6, J8, ?
Pattern: +2 letters, +2 numbers
Next: J + 4 = N, 8 + 2 = 10 → N10
3. ALPHANUMERIC SERIES
Type 1: Letter–Number Combined Pattern
Example (IPMAT):
Q13. A1, C3, F5, J7, ?
Letters: +2, +3, +4 (increasing skips)
Numbers: +2 each
Next letter skip = +5 → J + 5 = O
Next number = 7 + 2 = 9
Answer: O9
Type 2: Interleaved Letter–Number
Example:
Q14. 2A, 4C, 6E, 8G, ?
Numbers: +2
Letters: +2
Next = 10I
4. FIGURE SERIES (Non-Verbal)
(Useful for CUET & IPMAT)
Type 1: Rotation
Concept:
Figures rotate by fixed degrees (90°, 180°, etc.)
Example:
A triangle rotates 90° clockwise each step → next is the
next 90° rotation.
Type 2: Construction / Deconstruction
Concept:
Dots, lines, or shapes added or removed in pattern.
5. MISCELLANEOUS / SPECIAL SERIES
Type 1: Digit Manipulation Series
Example:
Q15. 13, 17, 23, 31, 41, ?
Observation: reversed primes or prime increments
Pattern: primes ending with 3,7,3,1,1…
Better pattern: +4, +6, +8, +10
Next = 41 + 12 = 53
Type 2: Difference of Square / Cube
Example:
Q16. 3, 10, 21, 36, 55, ?
Differences: 7, 11, 15, 19 → +4
Next difference = 23
Next term = 55 + 23 = 78
Previous Year Style – 10 Full Questions with Detailed
Solutions
Q17. (CUET 2023 )
6, 11, 21, 36, 56, ?
Solution:
Differences = 5, 10, 15, 20 → +5 pattern
Next diff = 25
Next = 56 + 25 = 81
Q18. (CLAT)
D, H, M, S, ?
Positions: 4,8,13,19 → +4, +5, +6
Next difference = +7
19 + 7 = 26 → Z
Q19. (IPMAT 2022)
5, 15, 45, 135, ?
×3 each step
Next = 135×3 = 405
Q20. (CUET logical reasoning)
7, 14, 28, 56, 112, ?
×2 pattern
Next = 112×2 = 224
Q21. (CLAT 2020)
AZ, CY, EX, GV, ?
A→C→E→G → +2
Z→Y→X→V → –1, –1, –2
Pattern suggests next: I + ?
Let's decode:
Steps of right letters: –1, –1, –2 → next should be –2
V – 2 = T
Left letters: +2 each: G +2 = I → IT
Q22. (IPMAT)
1, 4, 9, 18, 35, ?
Pattern:
1×1+3 = 4
2×2+5 = 9
3×3+9 = 18
4×4+19 = 35
Differences: 3,5,9,19 → doubling +1
Next = 5×5 + (19×2+1)
= 25 + (39) = 64
Q23. (CUET)
K, L, N, Q, U, ?
Positions: 11,12,14,17,21 → +1,+2,+3,+4
Next = +5 → 21 + 5 = 26 → Z
Q24. (CLAT)
2B, 4D, 8H, 16L, ?
Numbers: ×2
Letters: +2, +4, +4, +4
Pattern increases after first step
Next letter: L + 4 = P
Next = 32P
Q25. (IPMAT)
11, 13, 17, 23, 31, ?
Differences = 2,4,6,8 → +2 sequence
Next diff = 10
Next = 31 + 10 = 41
Q26. (CUET)
Q, R, T, W, A, ?
Positions:
Q(17), R(18), T(20), W(23), A(1 after Z = 27)
Differences: +1, +2, +3, +4
Next = +5
From A(27) + 5 = 32 → 32 - 26 = 6 → F
Some more questions for practice :
1.
(CUET 2023 – Based)
Find the next term:
7, 14, 28, 56, ?
a) 84
b) 102
c) 112
d) 224
Answer: d) 224
2. (IPMAT 2022 – Based)
5, 15, 45, 135, ?
a) 180
b) 405
c) 315
d) 540
Answer: b) 405
3. (CLAT – Based)
D, H, M, S, ?
a) X
b) Y
c) Z
d) U
Answer: c) Z
4.
3, 8, 15, 24, 35, ?
a) 44
b) 46
c) 48
d) 52
Answer: c) 48
5. (CUET-style)
4, 9, 6, 11, 8, 13, ?
a) 14
b) 15
c) 16
d) 18
Answer: b) 15
6. (CLAT PYQ-based)
Z, X, V, T, ?
a) P
b) Q
c) R
d) S
Answer: c) R
7.
A, C, F, J, O, ?
a) S
b) T
c) U
d) V
Answer: c) U
8.
1, 4, 9, 16, 25, ?
a) 30
b) 35
c) 36
d) 49
Answer: c) 36
9. (IPMAT based)
11, 13, 17, 23, 31, ?
a) 41
b) 43
c) 45
d) 47
Answer: a) 41
10. (CUET Style)
6, 11, 21, 36, 56, ?
a) 71
b) 76
c) 81
d) 86
Answer: c) 81
11. (Alphabet Series)
B, E, H, K, ?
a) M
b) N
c) O
d) P
Answer: b) N
12. (CUET 2022 – Based)
K, L, N, Q, U, ?
a) X
b) Y
c) Z
d) A
Answer: c) Z
13.
2, 6, 18, 54, ?
a) 108
b) 162
c) 216
d) 312
Answer: b) 162
14.
3, 10, 21, 36, 55, ?
a) 70
b) 73
c) 78
d) 85
Answer: c) 78
15. (Alphanumeric – IPMAT)
A1, C3, F5, J7, ?
a) L9
b) M9
c) N9
d) O9
Answer: d) O9
16.
Q, R, T, W, A, ?
a) D
b) E
c) F
d) G
Answer: c) F
17. (CLAT based)
AZ, CY, EX, GV, ?
a) IU
b) IT
c) HT
d) KT
Answer: b) IT
18.
13, 17, 23, 31, 41, ?
a) 47
b) 49
c) 51
d) 53
Answer: d) 53
19. (CUET Style)
12, 25, 51, 103, ?
a) 206
b) 207
c) 208
d) 210
Answer: b) 207
(×2 +1 pattern)
20.
A2, C4, F6, J8, ?
a) M10
b) N10
c) O10
d) P10
Answer: b) N10
21.
Z, W, S, N, ?
a) I
b) J
c) K
d) L
Answer: b) J
(–3, –4, –5, –6)
22.
8, 27, 64, 125, ?
a) 216
b) 225
c) 256
d) 343
Answer: a) 216
(Cubes)
23. (IPMAT - based)
14, 28, 20, 40, 32, ?
a) 48
b) 52
c) 56
d) 64
Answer: c) 56
(×2, ÷1.4 pattern alternate)
24.
19, 23, 31, 47, 71, ?
a) 89
b) 95
c) 105
d) 109
Answer: d) 109
(Prime series)
25. (CUET Non-verbal idea – numeric version)
3, 6, 12, 21, 33, ?
a) 42
b) 45
c) 48
d) 51
Answer: d) 51
(Differences: 3, 6, 9, 12 → +3)
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