Question

What is the sum of the geometric sequence -4, 24, -144, ... if there are 7 terms?

Answer 1

\(\LARGE S_n=\frac{a_1(1-r^n)}{1-r}\), where \(S_n\) is the sum, \(a_1\) is the term, r is the ratio and n is the number of terms.

you can find the ratio by diving a term by its previous term.

Answer 2

so like, -144/24?

Answer 3

yeah

Answer 4

Then once I hit the 7th term, I divide that by the previous term and I should get my answer?

Answer 5

what do you mean?

r= -144/24

then substitute what you get for r in the formula i typed above.
you are looking for \(S_7\).

you have \(a_1=-4\), \(n=7\), \(r=-144/24\)

Answer 6

Oh, I get it.

Answer 7

(^_^) so what did you get?

Answer 8

I got -159,964

Answer 9

yeah, you're right

Answer 10

Thanks!

Answer 11

no problem