The first term of a G.P. whose second term is | vedclass

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(C) Let the first term be $a$ and the common ratio be $r$.The second term of the $G.P.$ is given by $ar = 2$.The sum to infinity of a $G.P.$ is given

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$4$

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(C) Let the first term be $a$ and the common ratio be $r$.The second term of the $G.P.$ is given by $ar = 2$.The sum to infinity of a $G.P.$ is given by $S_{\infty} = \frac{a}{1 - r} = 8$,where $|r| From $ar = 2$,we have $a = \frac{2}{r}$.Substituting this into the sum formula: $\frac{2/r}{1 - r} = 8$.$\Rightarrow \frac{2}{r(1 - r)} = 8$.$\Rightarrow 2 = 8r(1 - r)$.$\Rightarrow 1 = 4r(1 - r)$.$\Rightarrow 4r^2 - 4r + 1 = 0$.This is a quadratic equation: $(2r - 1)^2 = 0$.Thus,$r = \frac{1}{2}$.Now,find the first term $a$: $a = \frac{2}{r} = \frac{2}{1/2} = 4$.Therefore,the first term is $4$.

The first term of a $G.P.$ whose second term is $2$ and sum to infinity is $8$,will be

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