What is the basic approach to solving Number and Letter Series questions in CAT exams?

Identify the pattern: Look for arithmetic progression, geometric progression, squares, cubes, alternate patterns, etc.

Observe differences: Note first-order and second-order differences.

Look for alternating or complex sequences.

For letters, check for alphabetical positions, gaps, and cyclic repetition.

Combine patterns if needed (e.g., numbers increasing while letters decrease).

What comes next in the series: 2, 6, 12, 20, 30, ?

Add consecutive even numbers: 
2 (+4) → 6 (+6) → 12 (+8) → 20 (+10) → 30 (+12) → 42

What comes next in the series: A, C, F, J, O, ?

Positions: A(1), C(3), F(6), J(10), O(15); 
differences: +2, +3, +4, +5 → next is +6 → 21 = U

Complete the series: 1, 4, 9, 16, ?, 36

Squares of natural numbers: 
1², 2², 3², 4², 5² = 25, 6²

Find the missing term: Z, X, U, Q, ?

Positions: Z(26), X(24), U(21), Q(17); 
differences: -2, -3, -4 → next: -5 → 17 - 5 = 12 = L

What comes next: 81, 27, 9, 3, ?

Dividing by 3 each time: 81 ÷ 3 = 27, and so on.

Complete the series: A, D, H, M, ?

Positions: A(1), D(4), H(8), M(13);
differences: +3, +4, +5 → next +6 → 13 + 6 = 19 = S

Find the missing term: 3, 6, 11, 18, ?

Differences: +3, +5, +7, +9 → next +11 → 18 + 11 = 29
Correction: Previous step:
3 → 6 (+3)
6 → 11 (+5)
11 → 18 (+7)
18 → ? (+9) → 18 + 9 = 27

Complete the series: B, D, G, K, ?

Positions: B(2), D(4), G(7), K(11); 
differences: +2, +3, +4 → next +5 → 11 + 5 = 16 = P

What comes next: 144, 121, 100, 81, ?

These are perfect squares in reverse: 
12², 11², 10², 9² → next: 8² = 64

Complete the series: 2, 3, 5, 8, 12, ?

Add 1, then 2, 3, 4…:
2 + 1 = 3

3 + 2 = 5

5 + 3 = 8

8 + 4 = 12

12 + 5 = 17

What letter comes next in the series: M, N, P, S, ?

Alphabet positions: M(13), N(14), P(16), S(19);
differences: +1, +2, +3 → next +4 → 19 + 4 = 23 = W

Find the next number: 2, 3, 7, 16, 32, ?

Differences:

3 - 2 = 1

7 - 3 = 4

16 - 7 = 9

32 - 16 = 16

Next difference: +25 → 32 + 25 = 57

Identify the next letter: Z, W, S, N, ?

Positions: Z(26), W(23), S(19), N(14);
differences: -3, -4, -5 → next: -6 → 14 - 6 = 8 = H

What comes next: 1, 1, 2, 3, 5, 8, ?

Fibonacci series: 1, 1, 2, 3, 5, 8 → 8 + 5 = 13

What comes next: C, F, J, O, ?

Position increments: +3, +4, +5, +6 → C(3) → F(6) → J(10) → O(15) → 15 + 6 = 21 = U