Question

Find the sum of the first 8 terms of the sequence.
1, -3, -7, -11, ...

Answer 1

You are subtracting four each time. 1-4=-3, -3-4=-7, etc. Find the next four terms by subtracting four from each term and once you have all eight, add them together.

Answer 2

wow thats way simpler than it seemed okay i got it!

Answer 3

what's the 8th term anyway?

Answer 4

-27

Answer 5

\(\huge a_n=a_1+8(n-1)d\) rings a bell?

Answer 6

woops... darn... ahemm one sec rather \(\huge a_n=a_1+(n-1)d\)

Answer 7

that's the equation for arithmetic sequences is it not?

Answer 8

yes

Answer 9

I assume you're doing sequences?

Answer 10

yeah, the answer is -107 I'm pretty sure. I'm not the best at math, I'm more of a bio-sceince girl myself so calc is hard for me

Answer 11

1, -3, -7, -11 <--- notice your common ratio, is -4 that is "d"

so \(\bf \Large a_n=a_1+(n-1)d\\ \quad \\
a_n=n^{th}\ term\qquad a_1=1^{st}\ term\qquad d=\textit{common ratio}\\ \quad \\
a_n=a_1+(n-1)d\implies \Large a_8=1+(8-1)(-4)\)

Answer 12

so now you know the 1st term and the 8th term, what's the sum?

well \(\Large \bf Sn=\cfrac{n}{2}(a_1+a_n)\implies S8=\cfrac{8}{2}(a_1+a_8)\)

Answer 13

hmm well... anyhow \(\bf \large S_n=\cfrac{n}{2}(a_1+a_n)\implies S_8=\cfrac{8}{2}(a_1+a_8)\)

Answer 14

\(\bf S_n=\cfrac{n}{2}(a_1+a_n)\implies S_8=\cfrac{8}{2}(a_1+a_8)\\ \quad \\
S_{\color{red}{ 8}}=\cfrac{{\color{red}{ 8}}}{2}(1+{\color{red}{ -27}})\)