In the sequence of numbers 5,8,15,20,29,40,53 one number is wrong. The wrong number is

Options

A. 15
B. 20
C. 29
D. 40

Answer

To determine the wrong number in the sequence 5, 8, 15, 20, 29, 40, 53, we will analyze the differences between consecutive terms and identify any inconsistencies.

### Step-by-Step Solution:

1. **List the Sequence**:
The given sequence is:
\[ 5, 8, 15, 20, 29, 40, 53 \]

2. **Calculate the Differences**:
We will calculate the differences between consecutive terms:
- \(8 - 5 = 3\)
- \(15 - 8 = 7\)
- \(20 - 15 = 5\)
- \(29 - 20 = 9\)
- \(40 - 29 = 11\)
- \(53 - 40 = 13\)

So, the differences are:
\[ 3, 7, 5, 9, 11, 13 \]

3. **Analyze the Differences**:
The differences should follow a pattern. Let's look at the differences:
- The first difference is \(3\).
- The second difference is \(7\).
- The third difference is \(5\).
- The fourth difference is \(9\).
- The fifth difference is \(11\).
- The sixth difference is \(13\).

Observing the differences, we notice that they should ideally increase by a consistent amount.

4. **Identify the Pattern**:
The expected pattern of differences appears to be:
- Start with \(3\), then add \(4\) for the next difference, which gives us \(7\).
- Continuing this pattern, we would expect the next difference to be \(11\) (which is \(7 + 4\)), and then \(15\) (which is \(11 + 4\)).

However, we see a discrepancy with \(5\) in the differences.

5. **Identify the Wrong Number**:
The difference of \(5\) (which corresponds to the transition from \(8\) to \(15\)) seems out of place. Instead, we would expect the difference to be \(11\) (which would mean the term should be \(19\) instead of \(15\)).

6. **Conclusion**:
Therefore, the wrong number in the sequence is:
\[ \text{The wrong number is } 15. \]