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

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(B) Let $r$ be the common ratio of the $G.P.$The first term is $a = 1$.The $n^{th}$ term of a $G.P.$ is given by $a_n = a r^{n-1}$.Thus,the third term

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$3$

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(B) Let $r$ be the common ratio of the $G.P.$The first term is $a = 1$.The $n^{th}$ term of a $G.P.$ is given by $a_n = a r^{n-1}$.Thus,the third term is $a_3 = a r^{3-1} = 1 \cdot r^2 = r^2$.The fifth term is $a_5 = a r^{5-1} = 1 \cdot r^4 = r^4$.Given that the sum of the third and fifth terms is $90$,we have:$r^2 + r^4 = 90$Rearranging the equation,we get:$r^4 + r^2 - 90 = 0$Let $x = r^2$. Then the equation becomes:$x^2 + x - 90 = 0$Factoring the quadratic equation:$(x + 10)(x - 9) = 0$This gives $x = -10$ or $x = 9$.Since $x = r^2$,$r^2$ cannot be negative for real numbers. Therefore,$r^2 = 9$.Taking the square root,we get $r = \pm 3$.

The first term of a $G.P.$ is $1$. The sum of the third and fifth terms is $90$. Find the common ratio of the $G.P.$ (in $, -3$)

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