Question

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

Answer 1

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`