the 2 and 3 term of GP is 24 and 12(x+1).If the sum of the first 3 terms is 76.Find the value of x


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Question Number 62016 by kiplangatryan89@gmail.com last updated on 14/Jun/19

$t h e 2 a n d 3 t e r m o f G P i s 24$ $a n d 12 (x + 1) . I f t h e s u m o f t h e$ $f i r s t 3 t e r m s i s 76 . F i n d t h e v a l u e$ $o f x$
Commented by Tony Lin last updated on 14/Jun/19

$r = \frac{12 (x + 1)}{24} = \frac{x + 1}{2}$ $S_{3} = a_{1} + a_{2} + a_{3} = \frac{48}{x + 1} + 24 + 12 (x + 1) = 76$ $\Rightarrow \frac{48}{x + 1} + 12 (x + 1) - 52 = 0$ $\Rightarrow 3 {(x + 1)}^{2} - 13 (x + 1) + 12 = 0$ $\Rightarrow [(x + 1) - 3] [3 (x + 1) - 4] = 0$ $\Rightarrow x + 1 = 3 o r x + 1 = \frac{4}{3}$ $\Rightarrow x = 2 o r x = \frac{1}{3}$
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