Q2 of 104 Page 491

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

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 = A²r^{2p - 2}

⇒ Ar^{p - 1} = (mn)^1/2

⇒ p^th term = (mn)^1/2

Ans: p^th term = (mn)^1/2

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