Question

What is the sum of the geometric sequence 1, −6, 36, … if there are 7 terms?

Answer 1

ITS POSITIVE 39991!!! The answer is D

Answer 2

Answer: The required sum is 39991.

Step-by-step explanation: We are given to find the sum of the following 7-term geometric sequence:

1, -6, 36, . . ..

Here, the first term , a = 1

and

common ratio, 'r' is given by

`d=(-6)/(1)=(36)/(-6)=~.~.~.=-6.`

We know that

the sum of first 'n' terms of a geometric sequence is given by

`S_n=(a(r^n-1))/(r-1),~r>1~~~~~~~~~\textup{or}~~~~~~~~~~~S_n=(a(1-r^n))/(1-r),~r<1.`

For the given geometric sequence, r = -6 < 1.

Therefore, the sum of first 7 terms will be

`S_7\\\\\\=(a(1-r^n))/(1-r)\\\\\\=(1(1-(-6)^7))/(1-(-6))\\\\\\=(1+279936)/(1+6)\\\\\\=(279937)/(7)\\\\\\=39991.`

Thus, the required sum is 39991.