Question

What is the sum of a 7-term geometric series if the first term is −6, the last term is −24,576, and the common ratio is −4?

Answer 1

check the attachment

Answer 2

The sum of the seven term geometric series is given as -19662

Step-by-step explanation:

The nth term of the geometric series is depicted by:

$a_{n}=a r^{n-1}$

Where,

$a_n$ is the nth term of the geometric series

r is the common ratio

The sum of the series is given by the formula given below:

$S=\left(a \frac{\left(1-r^{n}\right)}{(1-r)}\right)$

Substituting the given values gives us:

$S=(-6) \times\left(\frac{1-(-4)^{7}}{1-(-4)}\right)$

This can be solved as:

$S=(-6) \times \frac{16385}{5}$

Which further results into:

S = -19662