Question

What is the sum of an 8-term geometric series if the first term is 15 and the last term is -4,199,040? Answers to choose from.

a)-3,599,175
b)-3,359,230
c)-3,119,285
d)-2,879,340

Answer 1

well you need to find the common ratio 1st

the formula for a term in a geometric series is

\[T_{n} = ar^{n -1}\]

a = 1st term and r is the common ratio

so you know

\[-4199040 = 15\times r^{8 - 1}.... or -4199040 = 15 \times r^7\]

you need to solve for r as the 1st step.

Answer 2

ok

Answer 3

when you have found r

the sum is

\[S_{8} \frac{15(r^8 -1)}{r -1}\]

Answer 4

i have that formula and for the answer i got -3,119,285 @campbell_st is this correct?

Answer 5

what did you get for r..?

Answer 6

257

Answer 7

ummm big difference there

this is how I found r

\[\frac{-4199040}{15} = r^7\]

so

\[r = \sqrt[7]{\frac{-4199040}{15}}\]

try that and see what you get

Answer 8

ok

Answer 9

what did you get...?

Answer 10

257 idk know whats wrong

Answer 11

ok... what is

-4199040/15 =

Answer 12

-279936

Answer 13

thats correct now on your calculator enter

(-279936)^(1/7)

fractional powers are the same as taking the 7th root.

Answer 14

6

Answer 15

@campbell_st

Answer 16

umm it should be r - 6

Answer 17

opps r = -6

Answer 18

ohh ok my bad lol

Answer 19

ok... now you need to evaluate

\[S_{8} = \frac{15((-6)^8 -1)}{(-6 -1)}\]

you just need to evaluate the above...

and the answer should be negative...and please input it as its written... otherwise you won't get the right answer.

Answer 20

ok the answer i got this time is -2,879,340 is this correct?? @campbell_st

Answer 21

well i got -3599175 so you can choose.

Answer 22

okay thank you for the guidance

Answer 23

glad to help