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

Answer: 51 is the wrong number; the correct term should be 52.5.

Pattern: Each term is obtained by multiplying (previous term + 1) by k, where k starts at 0.5 and increases by 0.5 each step.

• Step 1: k = 0.5 → 0.5 × (7 + 1) = 0.5 × 8 = 4

• Step 2: k = 1.0 → 1 × (4 + 1) = 1 × 5 = 5

• Step 3: k = 1.5 → 1.5 × (5 + 1) = 1.5 × 6 = 9

• Step 4: k = 2.0 → 2 × (9 + 1) = 2 × 10 = 20

• Step 5 (correct next value): k = 2.5 → 2.5 × (20 + 1) = 2.5 × 21 = 52.5 (so 51 is incorrect)

• Step 6: k = 3.0 → 3 × (52.5 + 1) = 3 × 53.5 = 160.5

Conclusion: The sequence follows k = 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 with next = k × (previous + 1). Therefore 51 does not follow this rule and should be 52.5.