What will come in place of (?) in the following number series problems?
`15," "8," "9," "15," "32," "?`

Options

A. A)98
B. B)66
C. C)80.5
D. D)82.5

Answer

To solve the number series problem given as `15, 8, 9, 15, 32, ?`, we will analyze the pattern step by step.

### Step-by-Step Solution:

1. **Identify the first term**: The first term is 15.

2. **Calculate the second term**:
- We take the first term (15), add 1 to it:
\[ 15 + 1 = 16 \]
- Then we multiply by 0.5:
\[ 16 \times 0.5 = 8 \]
- Thus, the second term is 8.

3. **Calculate the third term**:
- We take the second term (8), add 1 to it:
\[ 8 + 1 = 9 \]
- Then we multiply by 1:
\[ 9 \times 1 = 9 \]
- Thus, the third term is 9.

4. **Calculate the fourth term**:
- We take the third term (9), add 1 to it:
\[ 9 + 1 = 10 \]
- Then we multiply by 1.5:
\[ 10 \times 1.5 = 15 \]
- Thus, the fourth term is 15.

5. **Calculate the fifth term**:
- We take the fourth term (15), add 1 to it:
\[ 15 + 1 = 16 \]
- Then we multiply by 2:
\[ 16 \times 2 = 32 \]
- Thus, the fifth term is 32.

6. **Calculate the sixth term (the missing term)**:
- We take the fifth term (32), add 1 to it:
\[ 32 + 1 = 33 \]
- Then we multiply by 2.5:
\[ 33 \times 2.5 = 82.5 \]
- Thus, the sixth term is 82.5.

### Conclusion:
The missing term in the series is **82.5**.