Question

Find the sum of an 8-term geometric sequence when the first term is 7 and the last term is 114,688 and select the correct answer below. 152,915 16,384 16,377 152,908

Answer 1

152,915

Explanation:

Answer 2

`a_1=7 \\ a_8=114688 \\ \\ a_n=a_1 * r^(n-1) \\ a_8=a_1 * r^7 \\ 114688=7 * r^7 \\ (114688)/(7)=r^7 \\ 16384=r^7 \\ r=\sqrt[7]{16384} \\ r=4 \\ \\ S_n=(a_1(1-r^n))/(1-r) \\ \Downarrow \\ S_8=(7(1-4^8))/(1-4)=(7(1-65536))/(-3)=(7 * (-65535))/(-3)=7 * 21845=152915`

The answer is 152,915.