In the following number series only one is wrong. Find out the wrong number.…

Answer: 51 is the wrong number.

Rule: Each term is obtained by multiplying the previous term by k and then adding k, where k increases by 0.5 each step (k = 0.5, 1, 1.5, 2, 2.5, 3, ...).

• 7 → 4: 7 × 0.5 + 0.5 = 4

• 4 → 5: 4 × 1 + 1 = 5

• 5 → 9: 5 × 1.5 + 1.5 = 9

• 9 → 20: 9 × 2 + 2 = 20

• 20 → 52.5 (expected): 20 × 2.5 + 2.5 = 52.5. The given term 51 is therefore incorrect.

• 52.5 → 160.5: 52.5 × 3 + 3 = 160.5

Conclusion: Replace 51 with 52.5 to make the sequence consistent; therefore 51 is the wrong number.