32 16 24 65 210 945 5197.5

Options

A. 945
B. 16
C. 24
D. 65

Explanation

To solve the problem of identifying the wrong number in the series: 32, 16, 24, 65, 210, 945, 5197.5, we will analyze the pattern step by step.

### Step-by-Step Solution:

1. **Identify the Series**:
The series given is:
\[ 32, 16, 24, 65, 210, 945, 5197.5 \]

2. **Look for a Pattern**:
We will check the relationship between consecutive numbers.

3. **First Pair (32 to 16)**:
\[ 32 \div 2 = 16 \]
This works.

4. **Second Pair (16 to 24)**:
\[ 16 \times 1.5 = 24 \]
This also works.

5. **Third Pair (24 to 65)**:
Here, we need to check if there's a multiplication factor:
\[ 24 \times 2.5 = 60 \quad \text{(not equal to 65)} \]
This indicates that 65 might be the wrong number.

6. **Fourth Pair (65 to 210)**:
We will check if 65 is indeed the wrong number by continuing the pattern:
\[ 65 \div 2 = 32.5 \quad \text{(not consistent)} \]
Instead, let's assume the next number should follow the pattern established earlier:
\[ 24 \times 2.5 = 60 \quad \text{(instead of 65)} \]

7. **Fifth Pair (60 to 210)**:
Continuing with our assumption:
\[ 60 \times 3.5 = 210 \]
This works.

8. **Sixth Pair (210 to 945)**:
\[ 210 \times 4.5 = 945 \]
This also works.

9. **Seventh Pair (945 to 5197.5)**:
\[ 945 \times 5.5 = 5197.5 \]
This works too.

10. **Conclusion**:
The number 65 does not fit the established pattern. The correct number in the series should be 60 instead of 65.

### Final Answer:
The wrong number in the series is **65**.