Question

What is the sum of the geometric sequence 3, 12, 48, … if there are 8 terms?

Answer 1

`a_2/a_1=12/3=4`

`a_3/a_2=48/12=4`

`implies` common ratio`=r=4` and first term`=a_1=3`
no: of terms`=n=8`

Sum of geometric series is given by
`Sum=(a_1(1-r^n))/(1-r)=(3(1-4^8))/(1-4)=(3(1-65536))/(-3)=(3(-65535))/(-3)=65535`

Hence, the sum of series is `65535`.