SOLUTION: Given the following sequence, find a100 -15,-8,-1,6,13

Algebra ->  Expressions-with-variables -> SOLUTION: Given the following sequence, find a100 -15,-8,-1,6,13      Log On


   

Question 750517: Given the following sequence, find a100
-15,-8,-1,6,13
Found 2 solutions by tommyt3rd, reviewermath:
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
-15,-8,-1,6,13 tells us that d=7,
%0D%0Aa%5B1%5D=-15%0D%0A

%0D%0Aa%5Bn%5D=a%5B1%5D%2B%28n-1%29d%0D%0A
%0D%0Aa%5B100%5D=-15%2B%28100-1%29%287%29%0D%0A

a%5B100%5D=678


:)

Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
In arithmetic sequence,
a%5Bn%5D+=+a%5B1%5D+%2B+%28n+-+1%29d where a%5Bn%5D = nth term, d = common difference
The first term of the sequence -15,-8,-1,6,13,... is -15 and the common difference is 7.
a%5Bn%5D+ = -15+%2B+%28n+-+1%29%287%29
a%5Bn%5D+ = 7n+-+22
The 100th term is
a%5B100%5D+=+7%28100%29+-+22 = highlight%28678%29