In each of the following questions a series is given. In each one term is wrong. Find out the wrong term
3, 4, 13, 38, 87, 166, 289

Options

A. 38
B. 13
C. 87
D. 166

Answer

To find the wrong term in the series 3, 4, 13, 38, 87, 166, 289, we will analyze the differences between consecutive terms and look for a pattern.

### Step-by-Step Solution:

1. **List the Terms**: Write down the series.
- Series: 3, 4, 13, 38, 87, 166, 289

2. **Calculate the Differences**: Find the differences between consecutive terms.
- 4 - 3 = 1
- 13 - 4 = 9
- 38 - 13 = 25
- 87 - 38 = 49
- 166 - 87 = 79
- 289 - 166 = 123

So, the differences are: 1, 9, 25, 49, 79, 123.

3. **Analyze the Differences**: Look for a pattern in the differences.
- The differences are: 1 (1^2), 9 (3^2), 25 (5^2), 49 (7^2), 79, 123.
- The first four differences are perfect squares of odd numbers: 1^2, 3^2, 5^2, 7^2.

4. **Identify the Expected Difference**: The next difference should follow the pattern of odd squares.
- The next odd number after 7 is 9, so the next difference should be 9^2 = 81.

5. **Determine the Correct Term**:
- If we add 81 to the last correct term (38), we should get the next term.
- 38 + 81 = 119 (which is not in the series).
- Instead, let's check the difference from 87 to 166. The difference is 79, which is incorrect as it should have been 81.

6. **Conclusion**: The term 166 is incorrect because the difference from 87 should be 81, leading to the next term being 168 instead of 166.

### Final Answer:
The wrong term in the series is **166**.