Question

Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of the first 8 terms of the geometric sequence: -8, -16, -32, -64, -128, . . . .

A. -2003

B. -2040

C. -2060

D. -2038

Answer 1

So (if I remember it correctly) you would first find the common ratio first...what is the common ratio here??

Answer 2

not quite....common ratio means...what pattern does this follow...

so to get from -8 to -16...you multiply by?
to get from -16 to -32 to you multiply by the same number which is again...?

Answer 3

2

Answer 4

@johnweldon1993

Answer 5

yes 2....

so that is our common ratio....our "r"

Now use this formula

\[a \frac{ 1 - r^n }{ 1-r }\]

I believe that is correct

So

n = the number of "terms" you want...a.k.a here it asks for your 8th term

r = 2 (like we just found out

so plug in 8 for your n's and plug in 2 for your r's

a btw is the first number in the sequence...a.k.a -8

So what will your equation look like now?

Answer 6

a = 1 - 2^-8/ 1 - 2

Answer 7

* yes it is correct btw :) * so follow those steps to get your answer...and let me know if I need to clarify something

Answer 8

CLOSE! but no...hang on

Answer 9

1st....it's not a = .....a is part of the equation....it multiplys to the entire equation

Answer 10

2nd.....-8 is not your n (i'm speaking of your 2^-8)

Answer 11

So think of it like this

ANSWER = 'a' TIMES (1-r^n)/(1-r)

where again...remember 'a' is the first number in the series....a = -8 for you

so try that again...

Answer 12

Still confused?

just remember

a = -8
r = 2
n = 8

Answer 13

thank you @johnweldon1993