Question

In the following series find the one number that is wrong
2, 3, 13, 37, 86, 167, 288

• A. 3
• B. 13
• C. 37
• D. 76

Answer 1

The Correct Option is B

To identify the wrong number in the series 2, 3, 13, 37, 86, 167, 288, we need to observe the pattern in the sequence. Let's analyze the progression between each number to establish a rule: 

We hypothesize that these numbers could follow a specific increment pattern, for which we calculate the differences between consecutive terms:

3 - 2 = 1

13 - 3 = 10

37 - 13 = 24

86 - 37 = 49

167 - 86 = 81

288 - 167 = 121

Observing these differences: 1, 10, 24, 49, 81, 121, we see they do not follow a simple arithmetic or geometric progression. However, further inspection shows a potential link to perfect squares:

1 = 12

10 does not match any perfect square increment pattern

24 does not match any perfect square increment pattern

49 = 72

81 = 92

121 = 112

To align this sequence towards perfect squares, the differences 10 and 24 must be corrected. Observe:

Assume the second difference should also reflect perfect square pattern:

1, 4, 9, 16, 25, etc., leads us to expect 4 after 1, replacing 10.

This correction fits a perfect square model where:

New sequence: 2, 3, (3+4)=7, 7+9=16, 16+16=32, 32+25=57, (following this adjusted logic)

The incorrect number is hence:

13