If the (p + q)th and (p – q)th terms of a GP are m and n respectively, find its pth term.
Let,
tp + q = m = Arp + q - 1 = Arp - 1rq
and
tp - q = n = Arp - q - 1 = Arp - 1r - q
We know that pth term = Arp - 1
∴ m × n = A2r2p - 2
⇒ Arp - 1 = (mn)1/2
⇒ pth term = (mn)1/2
Ans: pth term = (mn)1/2