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

Jun 19, 2018

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

Explanation:

"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

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

${S}_{20} = \frac{2 \cdot \left({2}^{20} - 1\right)}{2 - 1}$

${S}_{20} = 2 \cdot \left({2}^{20} - 1\right) = 2097150$