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# An infinite GP has its first term as x and sum is 6 , then which of the following is true?

$\begin{array}{1 1} x < -12 \\ -12 < x < 0 \\ 0 < x < 12 \\ x > 12 \end{array}$

Answer : (c) 0 < x < 12
Explanation : $S_{\infty}\;of\;a\;GP$
$S_{\infty}=\frac{a}{1-r}$
$6=\frac{x}{1-r}$
$r=\frac{6-x}{6}$
$Since\;it\;is\;an\;infinite\;series\;with\;S_{\infty}=6,\quad\;|r|<1$
$-1 < r <1$
$-1 < \frac{6-x}{6} <1$
$0 < r <12.$