Question

Q 5

Answer 1

Let the first of the G.P. be a and its common ratio be r.
Then,
(p+q)^th term = m ⇒ ar^p+q-1 = m

(p-q)^th term = n ⇒ ar^p-q-1 = n

Now,
m x n = ar^p+q-1 x ar^p-q-1 

= a² x r^p+q-1+p-q-1
= a² x r^2p-2
= a² x r^2(p-1)
= (a x r^p-1)²

⇒ ar^p-1 = `sqrt"mn"`

⇒ p^th term = t_p = `sqrt"mn"`