`{:(37,19,20,31.5,65,165),(21,(a),(b),(c),(d),(d)):}`
What will come in the place of (e) ?

Options

A. 105
B. 41
C. 110
D. 108

Explanation

To find the value that comes in place of (e) in the series `{:(37,19,20,31.5,65,165),(21,(a),(b),(c),(d),(e)):}`, we need to analyze the first series and then apply the same pattern to the second series.

### Step-by-Step Solution:

1. **Identify the pattern in the first series (37, 19, 20, 31.5, 65, 165)**:
- From 37 to 19: The operation is \( 37 \times 0.5 + 0.5 = 19 \).
- From 19 to 20: The operation is \( 19 + 1 = 20 \).
- From 20 to 31.5: The operation is \( 20 \times 1.5 + 1.5 = 31.5 \).
- From 31.5 to 65: The operation is \( 31.5 \times 2 + 2 = 65 \).
- From 65 to 165: The operation is \( 65 \times 2.5 + 2.5 = 165 \).

So, the pattern involves alternating between multiplying by a factor and adding a constant.

2. **Apply the same pattern to the second series (21, (a), (b), (c), (d), (e))**:
- Start with 21:
- For (a): \( 21 \times 0.5 + 0.5 = 10.5 + 0.5 = 11 \).
- For (b): \( 11 \times 1 + 1 = 11 + 1 = 12 \).
- For (c): \( 12 \times 1.5 + 1.5 = 18 + 1.5 = 19.5 \).
- For (d): \( 19.5 \times 2 + 2 = 39 + 2 = 41 \).
- For (e): \( 41 \times 2.5 + 2.5 = 102.5 + 2.5 = 105 \).

Thus, the value that comes in place of (e) is **105**.