9, 13, 21, 37, 61, 133

Options

A. 61
B. 37
C. 21
D. 13

Explanation

To solve the series: 9, 13, 21, 37, 61, 133, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the first term and the next terms**:
- The first term is 9.

2. **Calculate the difference between consecutive terms**:
- 13 - 9 = 4
- 21 - 13 = 8
- 37 - 21 = 16
- 61 - 37 = 24
- 133 - 61 = 72

3. **Observe the differences**:
- The differences are: 4, 8, 16, 24, 72.

4. **Identify the pattern in the differences**:
- The first difference (4) can be expressed as \(2^2\).
- The second difference (8) can be expressed as \(2^3\).
- The third difference (16) can be expressed as \(2^4\).
- The fourth difference (24) does not fit the pattern, but we can check if it should be \(2^5\) which is 32.
- The last difference (72) does not fit the pattern either, but we can check if it should be \(2^6\) which is 64.

5. **Calculate what the next term should be**:
- If we follow the pattern correctly, after 37, we should add \(2^5 = 32\):
- 37 + 32 = 69 (this should be the next term instead of 61).

6. **Check the next term**:
- After 69, we should add \(2^6 = 64\):
- 69 + 64 = 133 (this matches the last term in the series).

7. **Identify the incorrect term**:
- The term 61 should be replaced with 69 to maintain the pattern.

### Final Answer:
The incorrect term in the series is **61**, and it should be replaced with **69**.

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