Direction : Series I: 8, 9, 15, 25, 42, 68, 105 Series II: 60, 180, 450, 900,…

Concept

In a 'wrong-term' number series, every term is generated from the previous term by one fixed rule. Find the rule that fits the majority of the gaps; the single term that does not obey it is the wrong term. Here each step adds a value of the form n2 + 1, where n = 1, 2, 3, … counts the steps.

Application

Apply term(next) = term(prev) + (n2 + 1) to Series I starting from 8:

1. 8 + (12 + 1) = 8 + 2 = 10

2. 10 + (22 + 1) = 10 + 5 = 15

3. 15 + (32 + 1) = 15 + 10 = 25

4. 25 + (42 + 1) = 25 + 17 = 42

5. 42 + (52 + 1) = 42 + 26 = 68

6. 68 + (62 + 1) = 68 + 37 = 105

The rule rebuilds the series as 8, 10, 15, 25, 42, 68, 105. Comparing with the given 8, 9, 15, 25, 42, 68, 105, only the second term differs: it is given as 9 but should be 10. So the wrong term is 9.

Cross-check

The question asks: the wrong term is the perfect square of which given option value? The wrong term is 9, and 9 = 32. So the required number is 3. As a contrast, 42 = 16, 52 = 25, 72 = 49, 82 = 64 — none of these equals 9.

Therefore the answer is 3.