Find the 8th term... 3, 11, 31, 69, 131,....

Series:

3, 11, 31, 69, 131, …

Step 1: First differences

11 − 3 = 8

31 − 11 = 20

69 − 31 = 38

131 − 69 = 62

So differences: 8, 20, 38, 62

Step 2: Second differences

20 − 8 = 12

38 − 20 = 18

62 − 38 = 24

These increase by +6 each time:

12 → 18 → 24 → next = 30

Step 3: Predict next first difference

Next first difference = 62 + 30 = 92

So:

6th term = 131 + 92 = 223

But we need the 8th term, so continue.

Next second difference after 30:

30 + 6 = 36

Next first difference = 92 + 36 = 128

7th term = 223 + 128 = 351

Next second difference after 36:

36 + 6 = 42

Next first difference = 128 + 42 = 170

8th term = 351 + 170 = 521

Correct answer: [B] 521