Question

Find the sum of the first 8 terms of the sequence. Show all work for full credit.

1, -3, -7, -11, ...

Answer 1

Try to find a pattern connecting each number, start simple. Is there any number I can add/subtract from 1 to get -3? Does this same rule hold for -3 to -7?

Answer 2

i see differences of -2, -4, -6. i see the pattern. but isn't there something else I have to do?

Answer 3

a=1
d=-3-1=-4
It is an A.P.
\[Sn=\frac{ n }{2 }\left\{ 2 a+\left( n-1 \right)d \right\}\]
n=8, Put the values and get the result.

Answer 4

Once you have the pattern, you can come up with a rule. For this problem, if you subtract 3 from each term, you will get the next term:

\[ (1-4) = -3, (-3-4) = -7, etc \]

So our rule can be:
\[ -3n+1 \]
where n starts at zero, so, plug in n = 0 to 7 to get the first 8 terms

Answer 5

-4n+1 is the rule, sorry for the typo

Answer 6

ohhh. i believe I understand it now. thanks :)