The `(m+n)t ha n d(m-n)t h` terms fa G.P. ae `pa n dq` respectively. Show that the mth and nth terms are `sqrt(p q)a n dp(q/p)^(m//2n)` respectively.

Explanation

Let `a` is the first term of the G.P. is `a` and the common ratio is `r`.

Then, it is given that ,

`ar^(m+n-1) = p->(1)`

`ar^(m-n-1) = q->(2)`

Multiplying (1) and (2),

`a^2r^(m+n-1+m-n-1) = pq`

`=>a^2r^(2(m-1)) = pq`

`=>ar^(m-1) = sqrt(pq)`

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