`{:(7,6,10,27,104,515),(9,(a),(b),(c),(d),(e)):}`
What will come in place of (d) ?

Options

A. 152
B. 156
C. 108
D. 112

Explanation

To solve the problem, we need to identify the pattern in the first series and then apply that pattern to the second series to find the value of (d).

### Step-by-Step Solution:

1. **Identify the Pattern in the First Series:**
The first series is: 7, 6, 10, 27, 104, 515.
- From 7 to 6: \( 7 - 1 = 6 \)
- From 6 to 10: \( 6 \times 2 - 2 = 10 \)
- From 10 to 27: \( 10 \times 3 - 3 = 27 \)
- From 27 to 104: \( 27 \times 4 - 4 = 104 \)
- From 104 to 515: \( 104 \times 5 - 5 = 515 \)

The pattern observed is:
- The first number is decreased by 1.
- Each subsequent number is obtained by multiplying the previous number by an increasing integer (2, 3, 4, 5...) and then subtracting the same integer.

2. **Apply the Pattern to the Second Series:**
The second series starts with: 9, (a), (b), (c), (d), (e).
- For (a): \( 9 \times 1 - 1 = 8 \)
- For (b): \( 8 \times 2 - 2 = 14 \)
- For (c): \( 14 \times 3 - 3 = 39 \)
- For (d): \( 39 \times 4 - 4 = 152 \)
- For (e): \( 152 \times 5 - 5 = 755 \)

3. **Conclusion:**
The value that comes in place of (d) is **152**.