Question

find r for the geometric series with s5=484, a1=4, and a5= 324

Answer 1

Summation of a geometric series is \(\large S_n = \frac{a_1(1-r^n)}{1-r}\) You are trying to find r. Let's substitute values and then rearrange.

Answer 2

\[\large 484 = \frac{4(1-r^5)}{1-r}\]\[484 (1-r)=4(1-r^5)\]\[484 - 484r = 4- 4r^5\]\[-484r +4r^5 =4-484\]