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Nth Term of GP

The fourth, s...

Question

The fourth, seventh and tenth terms of a G.P. are $p, q$ and $r$ respectively, then

p^{2} = q^{2} + r^{2}

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q^{2} = p r

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p^{2} = q r

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p q r + p q + 1 = 0

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Solution

The correct option is B $q^{2} = p r$
Let the first term of the G.P. is a and the common ratio is x
Now according to question
$a x^{3} = p$ , $a x^{6} = q$ , $a x^{9} = r$
Now by observing the equations we can conclude that
$q^{2} = a^{2} x^{12} = p r$

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