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

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(C) Given that the second term $ar = 2$ and the sum to infinity $S_{\infty} = \frac{a}{1-r} = 8$.From $ar = 2$,we get $a = \frac{2}{r}$.Substituting t

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$4$

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(C) Given that the second term $ar = 2$ and the sum to infinity $S_{\infty} = \frac{a}{1-r} = 8$.From $ar = 2$,we get $a = \frac{2}{r}$.Substituting this into the sum formula: $\frac{2/r}{1-r} = 8$.$\Rightarrow \frac{2}{r(1-r)} = 8$.$\Rightarrow 1 = 4r(1-r)$.$\Rightarrow 4r^2 - 4r + 1 = 0$.This is a quadratic equation $(2r - 1)^2 = 0$,which gives $r = \frac{1}{2}$.Substituting $r = \frac{1}{2}$ into $a = \frac{2}{r}$,we get $a = \frac{2}{1/2} = 4$.Thus,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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