Question

If the (p + q)^th and (p – q)^th terms of a GP are m and n respectively, find its p^th term.

Answer 1

Let, 

t_{p + q} = m = Ar^{p + q - 1} = Ar^{p - 1} r ^q 

And 

t_{p - q} = n = Ar^{p - q - 1} = Ar^{p - 1} r ^{- q} 

We know that p^th term = Ar^{p - 1} 

∴ m × n = A² r^{2p - 2} 

⇒ Ar^{p - 1} = (mn)^1/2 

⇒ p^th term = (mn)^1/2