If `p^(t h),\ q^(t h),\ r^(t h)a n d\ s^(t h)` terms of an A.P. are in G.P., then show that `(p-q),\ (q-r),\ (r-s)` are also in G.P.

Explanation

To solve the problem, we need to show that if the Pth, Qth, Rth, and Sth terms of an arithmetic progression (AP) are in geometric progression (GP), then the differences (p - q), (q - r), and (r - s) are also in GP.

### Step-by-step Solution:

1. **Define the AP Terms**:
Let the first term of the AP be \( A \) and the common difference be \( D \). Therefore, the Pth, Qth, Rth, and Sth terms of the AP can be expressed as:
- \( A_P = A + (P - 1)D \)
- \( A_Q = A + (Q - 1)D \)
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