The first term of a G.P. is 1. The sum of the | vedclass

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(C) Let $a$ be the first term and $r$ be the common ratio of the $G.P.$Given $a = 1$.The third term $a_3 = ar^2 = r^2$ and the fifth term $a_5 = ar^4

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$\pm 3$

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(C) Let $a$ be the first term and $r$ be the common ratio of the $G.P.$Given $a = 1$.The third term $a_3 = ar^2 = r^2$ and the fifth term $a_5 = ar^4 = r^4$.According to the problem,$a_3 + a_5 = 90$.So,$r^2 + r^4 = 90$,which implies $r^4 + r^2 - 90 = 0$.Let $x = r^2$. Then $x^2 + x - 90 = 0$.Factoring the quadratic equation: $(x + 10)(x - 9) = 0$.This gives $x = -10$ or $x = 9$.Since $x = r^2$ must be non-negative for real $r$,we have $r^2 = 9$.Therefore,$r = \pm 3$.

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

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