⇒ Let the first term be a and the common ratio be r.

∴ According to the question,

a_m+n = p.

a_m-n = q.

a_n = ar^n-1

a_m+n = a.r^m+n-1

a_m-n = a.r^m-n-1

∴ a.r^m+n-1 = p.

a.r^m-n-1 = n.

Multiplying above two equations we get

a²r^{(m+n-1+(m-n-1)} = a²r^(2m-2)

a²r^(2m-2) = p.q

(ar)^2(m-1) = p.q

∴ ar^m-1 =√p.q

⇒ M^th term is given by a.r^m-1

∴ ar^m-1 =√p.q