Consider the series: 8, 9, 15, 25, 42, 68, 105.

Identify the wrong term in the series and determine the nearest square number of which given term it corresponds to.

Question

Consider the series: 8, 9, 15, 25, 42, 68, 105.

Identify the wrong term in the series and determine the nearest square number of which given term it corresponds to.

Accepted Answer

**Solution:**

1. The given series is: 8, 9, 15, 25, 42, 68, 105.

2. Let's check the differences between consecutive terms:
   - 9 - 8 = 1
   - 15 - 9 = 6
   - 25 - 15 = 10
   - 42 - 25 = 17
   - 68 - 42 = 26
   - 105 - 68 = 37

3. The differences do not follow a consistent pattern. Let's consider the possibility that the second term is incorrect.

4. If we replace 9 with 10, the series becomes: 8, 10, 15, 25, 42, 68, 105.

5. Now, calculate the differences:
   - 10 - 8 = 2
   - 15 - 10 = 5
   - 25 - 15 = 10
   - 42 - 25 = 17
   - 68 - 42 = 26
   - 105 - 68 = 37

6. The differences are: 2, 5, 10, 17, 26, 37.
   These are increasing by consecutive odd numbers: +3, +5, +7, +9, +11.

7. Hence, the correct second term should be 10 instead of 9.

8. The wrong term 9 is the nearest square number of 3 squared (i.e., $3^2 = 9$).

9. Among the options, 5 corresponds to the term whose nearest square is 9 (since 5 squared is 25, but here the question asks which term's nearest square is the wrong term).

10. The wrong term 9 is the nearest square of 3, which corresponds to the 5th term in the series pattern.

**Answer:** (a) 5

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