Alphabetical & Number Series

Alphabetical Series

• Positions: A=1 … Z=26.
• EJOTY = 5, 10, 15, 20, 25.
• Opposite letter: position + opposite position = 27 (A↔Z, M↔N).
• From the right: 27 − position from the left.
• Letters between two letters: difference − 1.
• Method: convert letters to numbers, find the pattern, convert back. After Z, wrap around to A.
• Always check: alternate terms (two series mixed), letter groups, and pairs (AZ, BY, CX → DW).

Number Series

Numbers to Memorize

Squares	Cubes	Primes
1, 4, 9, 16, 25, 36, 49, 64, 81, 100	1, 8, 27, 64, 125, 216, 343, 512, 729, 1000	2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Square Values: 11²=121, 12²=144, 13²=169, 14²=196, 15²=225, 16²=256, 17²=289, 18²=324, 19²=361, 20²=400.

Patterns

Pattern	Example	Next
Constant difference (arithmetic)	5, 9, 13, 17	21
Constant ratio (geometric)	2, 6, 18, 54	162
Increasing differences	2, 3, 5, 8, 12 (+1, +2, +3, +4)	17
Second-order differences	1, 4, 10, 20, 35 (diffs 3, 6, 10, 15)	56
Squares / cubes	1, 4, 9, 16	25
n² ± k or n³ ± k	2, 5, 10, 17 (n²+1)	26
n(n+1)	2, 6, 12, 20, 30	42
×a + b	3, 7, 15, 31 (×2+1)	63
Increasing multipliers	1, 1, 2, 6, 24 (×1, ×2, ×3, ×4)	120
Fibonacci (sum of previous two)	1, 1, 2, 3, 5, 8	13
Prime numbers	2, 3, 5, 7, 11	13
Alternating series	2, 5, 4, 10, 6, 15	8

Steps

1. Find the differences between consecutive terms.
2. If differences are not constant, find the differences of differences.
3. If numbers grow fast, check the ratio (×2, ×3) or ×a + b.
4. If the numbers look like perfect squares or cubes, compare them to n², n³ (±1, ±2).
5. If the series looks messy, split it into odd and even terms.
6. Look for mixed operations (+, ×, alternately) or digit-based rules (sum of digits, reversing).

Wrong Number Series

Have to find the pattern from the terms that clearly fit, then identify the one that breaks it.

Example: 3, 6, 12, 24, 50, 96 → the pattern is ×2, so 50 should be 48.

Missing Number Tips

• Large jumps: think multiplication or squares/cubes.
• Small steady growth: think addition or differences.
• Ends in the same digits repeatedly: check cubes or multiples.
• Two numbers per step: treat as two interleaved series.

Mixed Alphanumeric Series

Have to handle letters and numbers separately, then combine.

• A1, C3, E5, ? → letters +2, numbers +2 → G7
• B2, D4, G7, K11, ? → letters +2, +3, +4, +5 → P; numbers +2, +3, +4, +5 → 16 → P16
• A2, C6, E18, ? → letters +2; numbers ×3 → G54

Practice Questions

1. Find the next term: B, E, I, N, T, ?

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

Answer: (c) A
Explanation: Positions are 2, 5, 9, 14, 20. The differences are +3, +4, +5, +6, so the next is +7. 20 + 7 = 27 = A.

2. How many letters are there between F and S in the English alphabet?

(a) 11
(b) 12
(c) 13
(d) 14

Answer: (b) 12
Explanation: F = 6, S = 19. Letters between = 19 − 6 − 1 = 12.

3. Which letter is the 7th from the right end of the alphabet?

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

Answer: (c) T
Explanation: Position from the left = 27 − 7 = 20, and the 20th letter is T.

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

(a) EV
(b) EU
(c) FV
(d) FU

Answer: (a) EV
Explanation: The first letter moves forward (A, B, C, D, E) and the second moves backward (Z, Y, X, W, V).

5. Find the next number: 2, 6, 12, 20, 30, ?

(a) 40
(b) 42
(c) 44
(d) 36

Answer: (b) 42
Explanation: The terms follow n(n+1): 1×2, 2×3, 3×4, 4×5, 5×6, so the next is 6×7 = 42. Equivalently, the differences are +4, +6, +8, +10, so the next is +12 (30 + 12 = 42).

6. Find the next number: 3, 7, 15, 31, 63, ?

(a) 125
(b) 126
(c) 127
(d) 128

Answer: (c) 127
Explanation: The rule is ×2 + 1. 3×2+1 = 7, 7×2+1 = 15, 15×2+1 = 31, 31×2+1 = 63, so 63×2+1 = 127.

7. Find the wrong number: 1, 4, 9, 16, 26, 36, 49

(a) 9
(b) 16
(c) 26
(d) 36

Answer: (c) 26
Explanation: The series is perfect squares: 1², 2², 3², 4², 5², 6², 7². The 5th term should be 5² = 25, not 26.

8. Find the next term: A, Z, C, X, E, V, ?

(a) F
(b) G
(c) T
(d) U

Answer: (b) G
Explanation: Two series are mixed. Odd terms: A, C, E, G (+2 each). Even terms: Z, X, V, T (−2 each). The next term is the 7th, which belongs to the odd series, so it is G.

9. Find the next term: C4, F9, I16, L25, ?

(a) O30
(b) O36
(c) P36
(d) N36

Answer: (b) O36
Explanation: Letters: C, F, I, L, O (+3 each). Numbers: 4, 9, 16, 25, 36, which are the squares of 2, 3, 4, 5, 6. So the next term is O36.

10. Find the next number: 2, 5, 4, 10, 6, 15, 8, ?

(a) 10
(b) 18
(c) 20
(d) 25

Answer: (c) 20
Explanation: Split into odd and even positions. Odd-position terms: 2, 4, 6, 8 (+2 each). Even-position terms: 5, 10, 15, 20 (+5 each). The 8th term is in the even series, so it is 20.