Question

The p+q term of a GP is m and its p-q term is n show that its p term=√mn.

Answer 1

A = a.r ^ (p+q-1)
B = a.r^ (p-q-1)
pth term = ar^(p-1)
If you multiply A and B terms you get
AB = a^2 x r^(2p-2)
AB = (ar^p-1)^2
ar^p-1 is the pth term of gp
AB ^2 of pth term, hence √AB is the pth term