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

−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

$r = \frac{15}{ - 3} = - 5$

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:

$S_7= - 39603$