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

Answer: 106.5 is the wrong number.

Reasoning:

• Write the series: 7, 4, 5, 9, 20, 51, 106.5

• Compute consecutive differences: 4 − 7 = −3; 5 − 4 = 1; 9 − 5 = 4; 20 − 9 = 11; 51 − 20 = 31.

• From the second difference onward, each difference equals three times the previous difference plus a small adjustment. The adjustments observed are +1, −1, −2: 1 → 4 = 3×1 + 1; 4 → 11 = 3×4 − 1; 11 → 31 = 3×11 − 2.

• Continue the adjustment pattern (next adjustment −3): next difference = 3×31 − 3 = 90, so the next term after 51 should be 51 + 90 = 141.

• Because the given final term 106.5 does not equal 141, 106.5 is the incorrect number. Replacing 106.5 with 141 restores the pattern.

Note: the correct answer choice should be the one that contains the number 106.5 (the incorrect term identified above).