6 7 9 13 26 37 69

Options

A. 7
B. 26
C. 69
D. 37

Explanation

To identify the odd one out in the series: 6, 7, 9, 13, 26, 37, 69, we will analyze the differences between consecutive numbers and look for a pattern.

### Step-by-Step Solution:

1. **List the Series**:
We start with the series:
\[ 6, 7, 9, 13, 26, 37, 69 \]

2. **Calculate Differences**:
We will find the difference between each consecutive pair of numbers:
- \( 7 - 6 = 1 \)
- \( 9 - 7 = 2 \)
- \( 13 - 9 = 4 \)
- \( 26 - 13 = 13 \)
- \( 37 - 26 = 11 \)
- \( 69 - 37 = 32 \)

So, the differences are:
\[ 1, 2, 4, 13, 11, 32 \]

3. **Analyze the Differences**:
Now, let's look for a pattern in the differences:
- The first three differences are \(1, 2, 4\), which are \(1 \times 2, 2 \times 2\).
- The next expected difference should logically be \(4 \times 2 = 8\).

4. **Identify the Anomaly**:
The difference between \(13\) and \(26\) is \(13\) instead of \(8\). This indicates that \(26\) does not fit the pattern.

5. **Correct the Series**:
If we replace \(26\) with \(21\) (which is \(13 + 8\)), we can check the new differences:
- \( 21 - 13 = 8 \)
- \( 37 - 21 = 16 \)

Now the differences are:
\[ 1, 2, 4, 8, 16, 32 \]
This follows the pattern of doubling each time.

6. **Conclusion**:
The number that does not fit the pattern in the series is \(26\). The correct number should be \(21\).

### Final Answer:
The odd one out in the series is **26**. It should be replaced by **21**.

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