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

1 Answer
sankarankalyanam
Jun 19, 2018

color(indigo)(S_(20) = (a (r^n-1)) / (r - 1) = 2097150

Explanation:

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

"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 = a_2 / a = a_3 / a_2 = 4/2 = 8/4 = 2

S_(20) = (2 * (2^(20) - 1)) / (2 -1)

S_(20) = 2 * (2^(20) - 1) = 2097150

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