The `(m+n)th and (m-n)th` terms of a G.P. are `p and q` respectively. Show that the mth and nth terms are `sqrt(p q) and p(q/p)^(m//2n)` respectively.

Explanation

To solve the problem, we need to show that the m-th and n-th terms of a geometric progression (G.P.) are \(\sqrt{pq}\) and \(p\left(\frac{q}{p}\right)^{\frac{m}{2n}}\) respectively, given that the \((m+n)\)-th term is \(p\) and the \((m-n)\)-th term is \(q\).

### Step-by-Step Solution:

1. **Write the expressions for the given terms in G.P.:**
The general term of a G.P. can be expressed as:
\[
a_k = a \cdot r^{k-1}
...