If the $(p + q)^{t h}$ term of a G.P. is m and $(p - q)^{t h}$ term is n, then pth term will be _____.

$(\frac{m}{n})$

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$(m - n)$

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$m n$

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$\sqrt{m n}$

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Solution

The correct option is D
$\sqrt{m n}$

Let $T_{p}$ be the $p^{t h}$ term of G.P

$T_{p + q} = a r^{p + q - 1} = m . . . (1) T_{p - q} = a r^{p - q - 1} = n . . . (2) T_{p} = a r^{p - 1} . . . (3)$

Multiplying (1) and (2)

$m n = a^{2} r^{2 p - 2} = (a r^{p - 1})^{2}$

$\Rightarrow T_{p} = a r^{p - 1} = \sqrt{m n}$

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