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Question

If the $p to the power of t h end exponent comma blank q to the power of t h end exponent$ , and $r to the power of t h end exponent$ terms of an A.P. are in G.P., then common ratio of the G.P. is

$\frac{p r}{q^{2}}$
$\frac{r}{p}$
$\frac{q + r}{p + q}$
$\frac{q - r}{p - q}$

The correct answer is: $fraction numerator q minus r over denominator p minus q end fraction$

$p to the power of t h end exponent comma blank q to the power of t h end exponent comma blank r to the power of t h end exponent$ terms of A.P. are
$a plus open parentheses p minus 1 close parentheses d equals x$ (1)
$a plus open parentheses q minus 1 close parentheses d equals x R$ (2)
$a plus open parentheses r minus 1 close parentheses d equals x R to the power of 2 end exponent$ (3)
Where $R$ is common ratio of G.P.
Subtracting (2) from (3) and (1) from (2) and then dividing the former by the later, we have
$fraction numerator q minus r over denominator p minus q end fraction equals fraction numerator x R to the power of 2 end exponent minus x R over denominator x R minus x end fraction equals R$

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