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-

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}