If the sum of an infinite geometric series is | vedclass

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Question

(D) The sum of an infinite geometric series is given by the formula $S = \frac{a}{1-r}$,where $a$ is the first term and $r$ is the common ratio.
Give

Vedclass · Accepted Answer

$\frac{1}{16}$

Vedclass · Answer

(D) The sum of an infinite geometric series is given by the formula $S = \frac{a}{1-r}$,where $a$ is the first term and $r$ is the common ratio.
Given $S = \frac{4}{5}$ and $a = \frac{3}{4}$.
Substituting the values into the formula: $\frac{4}{5} = \frac{\frac{3}{4}}{1-r}$.
Multiplying both sides by $(1-r)$,we get $\frac{4}{5}(1-r) = \frac{3}{4}$.
$1-r = \frac{3}{4} 	imes \frac{5}{4} = \frac{15}{16}$.
$r = 1 - \frac{15}{16} = \frac{1}{16}$.

If the sum of an infinite geometric series is $\frac{4}{5}$ and its $1^{st}$ term is $\frac{3}{4}$,then its common ratio is

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