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

$d=\dfrac{-6}{1}=\dfrac{36}{-6}=~.~.~.=-6.$

We know that

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

$S_n=\dfrac{a(r^n-1)}{r-1},~r>1~~~~~~~~~\textup{or}~~~~~~~~~~~S_n=\dfrac{a(1-r^n)}{1-r},~r$

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

Therefore, the sum of first 7 terms will be

$S_7\\\\\\=\dfrac{a(1-r^n)}{1-r}\\\\\\=\dfrac{1(1-(-6)^7)}{1-(-6)}\\\\\\=\dfrac{1+279936}{1+6}\\\\\\=\dfrac{279937}{7}\\\\\\=39991.$

Thus, the required sum is 39991.