If the $p$ th term of a G.P. is $α$ and $q$ th term is $β$ then $n$ th term is

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${(\frac{α^{n - p}}{β^{n - q}})}^{\frac{1}{p - q}}$

${(\frac{α^{n - q}}{β^{n - p}})}^{\frac{1}{p - q}}$

${(\frac{α^{n - q}}{β^{n - p}})}^{\frac{1}{q - p}}$

${(\frac{α^{n - p}}{β^{n - q}})}^{\frac{1}{q - p}}$

answer is B.

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Detailed Solution

$α = a r^{p - 1}, β = a r^{q - 1} \frac{α}{β} = r^{p - q} \Rightarrow r = {(\frac{α}{β})}^{\frac{1}{p - q}} a_{n} = a r^{n - 1} = {(\frac{α^{n - p}}{β^{n - p}})}^{\frac{1}{p - q}}$

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