What is the sum of the geometric sequence 1, –6, 36, … if there are 6 terms?

1 Answer
Jan 25, 2016

The geometric sequence is 1,-6,36,....

a_2/a_1=(-6)/1=-6

a_3/a_2=36/-6=-6

implies common ratio=r=-6 and a_1=1

Sum of geometric series is given by

Sum=(a_1(1-r^n))/(1-r)

Where n is number of terms, a_1 is the furst term, r is the common ratio.

Here a_1=1, n=6 and r=-6

implies Sum=(1(1-(-6)^6))/(1-(-6))=(1-46656)/(1+6)=(-46655)/7=-6665

Hence, the sum is -6665