Question

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

Answer 1

`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 = 4/2 = 8/4 = 2`

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

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