Question

Find the sum of a finite geometric sequence from n = 1 to n = 7, using the expression -4(6)^n-1
111,325
526
782
223,948

Answer 1

answer choices:
111,325
526
782
223,948

Answer 2

\(\large\color{black}{\displaystyle \sum_{ n=1 }^{ 7 } -4(6)^{n-1} }\) is that a good interpretation of the question ?

Answer 3

I guess..

Answer 4

you can apply the same formula

Answer 5

\(\large\color{black}{\displaystyle \Large\color{black}{ \displaystyle {\rm \LARGE S}_{_{n}}=\frac{a_{_{n}}\left(1-r^{n}\right)}{1-r}} }\)

Answer 6

what do I plug in for r?

Answer 7

as n=1, you are multiplying 0 times , times 6.
as n=2, you are multiplying once times 6
as n=3, you are multiplying twice times 6
and on...

Answer 8

what is your common ratio ?

Answer 9

6

Answer 10

also, please go ahead and fix your answer choices:)

Answer 11

yes, r=6

Answer 12

what about n?

Answer 13

you want to find the sum of 7 terms (from n=1 to n=7)

Answer 14

so n is 7.

Answer 15

oh, in the formula I posted here, the a(n) was supposed to be a(1)

Answer 16

\(\bf\color{red}{\large\color{black}{\displaystyle \Large\color{black}{ \displaystyle {\rm \LARGE S}_{_{n}}=\frac{a_{_{1}}\left(1-r^{n}\right)}{1-r}} }}\)

Answer 17

ok thanks! can you please help me with one more problem?

Answer 18

\(\bf\color{black}{\displaystyle \Large\color{black}{ \displaystyle {\rm \LARGE S}_{_{n}}=\frac{(-4)\left(1-6^{7}\right)}{1-6}} }\)

Answer 19

what was your answer?

Answer 20

my answer was 223,948, am I right?

Answer 21

almsoy

Answer 22

how can you have a positive sum, when every term is negative ?

Answer 23

\(\rm\color{blue}{\href{http:///www.wolframalpha.com/input/?i=sum+from+1+to+7%2C+-4%286%29%5E%28n-1%29}{The~Sum~is....}}\)

Also, I can verify it, by plugging the formula into the calculator
\(\rm\color{green}{\href{http:///www.wolframalpha.com/input/?i=%28%28-4%29%C3%97%281-6%5E7%29%29%2F%281-6%29}{verification,~~by~~plugging~~in.}}\)

Answer 24

what answer did you get? (sorry I couldn't answer earlier, openstudy froze for some reason)

Answer 25

I got option D, but negative.
The correct answer is -223,948