7 4 5 9 20 51 160.5

Options

A. 4
B. 5
C. 9
D. 51

Explanation

To solve the problem, we need to identify the incorrect number in the series: 7, 4, 5, 9, 20, 51, 160.5. We will analyze the pattern in the series step by step.

### Step-by-Step Solution:

1. **Identify the Series**: The series is given as 7, 4, 5, 9, 20, 51, 160.5.

2. **Observe the Pattern**:
- The first number is 7, which is followed by a decrease to 4.
- Then, the numbers seem to increase: 4 to 5 (increase of 1), 5 to 9 (increase of 4), and then 9 to 20 (increase of 11).

3. **Check the Differences**:
- The difference between 4 and 5 is 1.
- The difference between 5 and 9 is 4.
- The difference between 9 and 20 is 11.
- The difference between 20 and 51 is 31.
- The difference between 51 and 160.5 is 109.5.

4. **Look for a Multiplicative Pattern**:
- From 4 to 5: \(4 \times 1 + 1 = 5\)
- From 5 to 9: \(5 \times 1.5 + 1.5 = 9\)
- From 9 to 20: \(9 \times 2 + 2 = 20\)
- From 20 to 51: \(20 \times 2.5 + 2.5 = 52.5\) (but we have 51 in the series)
- From 51 to 160.5: \(51 \times 3 + 3 = 160.5\)

5. **Identify the Incorrect Number**:
- We see that instead of getting 52.5 after 20, we have 51 in the series. This indicates that 51 is the incorrect number.

6. **Conclusion**:
- The correct number that should replace 51 is 52.5.

### Final Answer:
The incorrect number in the series is **51**, and it should be replaced with **52.5**.

---