If `sin theta,sqrt(2) (sintheta + 1),6 sin theta +6` are in GP, than the fifth term is

Options

A. 81
B. `81sqrt(2)`
C. 162
D. `162sqrt(2)`

Explanation

To solve the problem, we need to determine if the terms \( \sin \theta \), \( \sqrt{2} (\sin \theta + 1) \), and \( 6 \sin \theta + 6 \) are in a geometric progression (GP). If they are, we can find the fifth term of the sequence.

### Step-by-Step Solution:

1. **Identify the Terms**:
- Let \( a = \sin \theta \)
- Let \( b = \sqrt{2} (\sin \theta + 1) \)
- Let \( c = 6 \sin \theta + 6 \)
...