find the wrong term in the series
5, 10, 17, 24, 37, 50, 65

Options

A. 10
B. 17
C. 24
D. 37

Explanation

To find the wrong term in the series 5, 10, 17, 24, 37, 50, 65, we will analyze the differences between consecutive terms and identify any inconsistencies.

### Step-by-Step Solution:

1. **Identify the Series**: The given series is:
\[ 5, 10, 17, 24, 37, 50, 65 \]

2. **Calculate the Differences**: We will find the differences between consecutive terms:
- \(10 - 5 = 5\)
- \(17 - 10 = 7\)
- \(24 - 17 = 7\)
- \(37 - 24 = 13\)
- \(50 - 37 = 13\)
- \(65 - 50 = 15\)

So, the differences are:
\[ 5, 7, 7, 13, 13, 15 \]

3. **Analyze the Differences**: Now, we will analyze the differences:
- The first difference is \(5\).
- The second difference is \(7\).
- The third difference is also \(7\).
- The fourth difference jumps to \(13\).
- The fifth difference remains \(13\).
- The sixth difference increases to \(15\).

The differences do not follow a consistent pattern.

4. **Look for a Pattern**: If we assume a pattern in the differences, we can see that the differences seem to increase by 2 after certain terms. If we consider the differences as:
- First difference: \(5\)
- Second difference: \(7\) (should be \(7\))
- Third difference: \(9\) (should be \(9\))
- Fourth difference: \(11\) (should be \(11\))
- Fifth difference: \(13\) (should be \(13\))
- Sixth difference: \(15\) (should be \(15\))

5. **Identify the Wrong Term**: The term \(24\) should actually be \(26\) to maintain the pattern of differences:
- \(5 + 5 = 10\)
- \(10 + 7 = 17\)
- \(17 + 9 = 26\) (instead of \(24\))
- \(26 + 11 = 37\)
- \(37 + 13 = 50\)
- \(50 + 15 = 65\)

6. **Conclusion**: The wrong term in the series is \(24\). It should be replaced with \(26\).

### Final Answer:
The wrong term is **24**, and it should be replaced with **26**.