Question

Find the sum of the geometric sequence −3, 15, −75, 375, ... when there are 7 terms and select the correct answer below. −39,063 39,063 58,593 −58,593

Answer 1

Answer: A.

-39,063 :))

Explanation:

Answer 2

−39,063

EXPLANATION

The given geometric sequence is

-3,15,-75,375,...

The sum of the first n-terms of a geometric sequence is calculated using the formula;

`S_n = \frac{a(1 - {r}^(n)) }{1 - r}`

Where a=-3 is the first term of the geometric sequence and

`r = (15)/( - 3) = - 5`

is the common ratio of the sequence.

The sum of the first seven terms is

`S_7= \frac{ - 3(1 - {( - 5)}^(7)) }{1 - - 5}`

`S_7= \frac{ - 3(1 + {( 5)}^(7)) }{6}`

This simplifies to:

`S_7= - 39603`