Question

What is the sum of the geometric sequence 4, 12, 36 … if there are 9 terms?

Answer 1

`a_2/a_1=12/4=3`

`a_3/a_2=36/12=3`

`implies` common ratio`=r=3` and first term`=a_1=4`
no: of terms`=n=9`

Sum of geometric series is given by
`Sum=(a_1(1-r^n))/(1-r)`

`impliesSum=(4(1-3^9))/(1-3)=(4(1-19683))/(-2)=-2(-19682)=39364`

Hence, the sum of series is `39364`.