The common ratio of a G.P. is -frac{4}{5} and | vedclass

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(B) The formula for the sum to infinity of a $G.P.$ is given by $S_{\infty} = \frac{a}{1-r}$,where $a$ is the first term and $r$ is the common ratio.G

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$16$

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(B) The formula for the sum to infinity of a $G.P.$ is given by $S_{\infty} = \frac{a}{1-r}$,where $a$ is the first term and $r$ is the common ratio.Given,$r = -\frac{4}{5}$ and $S_{\infty} = \frac{80}{9}$.Substituting the values into the formula:$\frac{80}{9} = \frac{a}{1 - (-\frac{4}{5})}$$\frac{80}{9} = \frac{a}{1 + \frac{4}{5}}$$\frac{80}{9} = \frac{a}{\frac{9}{5}}$$a = \frac{80}{9} 	imes \frac{9}{5}$$a = 16$.Thus,the first term is $16$.

The common ratio of a $G.P.$ is $-\frac{4}{5}$ and the sum to infinity is $\frac{80}{9} .$ Find the first term.

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