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The first term of a $G . P$ is $1$ . The sum of the third term and fifth term is $90$ , then the common ratio of $G . P$

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Detailed Solution

a = 1

$a_{3} = a r^{2} = r^{2}$

$a_{5} = a r^{4} = r^{4}$

$r^{2} + r^{4} = 90$

$r^{4} + r^{2} - 90 = 0$

$r^{2} = \frac{- 1 \pm \sqrt{1 + 360}}{2}$

$= \frac{- 1 \pm \sqrt{361}}{2}$

$= \frac{- 1 \pm 19}{2}$

$= - 10$ (or) $9$

$∴$ $r = \pm 3$

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