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How do you find the sum of the geometric sequence 2,4,8...if there are 20 terms?

1 Answer

sankarankalyanam

Jun 19, 2018

$S_{20} = \frac{a (r^{n} - 1)}{r - 1} = 2097150$ $color(indigo)(S_(20) = (a (r^n-1)) / (r - 1) = 2097150$

Explanation:

![https://www.slideshare.net/flago_0719/geometric-sequence-65431750]( useruploads.socratic.org )

$S u m o f n t e r m s o f a G S = S_{n} = (a {(r)}^{n} - 1) \frac{)}{r - 1}$ $"Sum of n terms of a G S = S_n = (a (r)^n-1 ))/ (r-1)$

where a is the first term, n the no. of terms and r the common ratio

$a = 2, n = 20, r = \frac{a_{2}}{a} = \frac{a_{3}}{a_{2}} = \frac{4}{2} = \frac{8}{4} = 2$ $a = 2, n = 20, r = a_2 / a = a_3 / a_2 = 4/2 = 8/4 = 2$

$S_{20} = \frac{2 \cdot (2^{20} - 1)}{2 - 1}$ $S_(20) = (2 * (2^(20) - 1)) / (2 -1)$

$S_{20} = 2 \cdot (2^{20} - 1) = 2097150$ $S_(20) = 2 * (2^(20) - 1) = 2097150$

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