SOLUTION: 1)The sum of the first 13 terms in arithmetic sequence is 1,475.5 while 131 is known to be the 8th term. Find the first term and common difference of this sequence?

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Question 964283: 1)The sum of the first 13 terms in arithmetic sequence is 1,475.5 while 131 is known to be the 8th term. Find the first term and common difference of this sequence?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
1)The sum of the first 13 terms in arithmetic sequence is 1,475.5 
n=13, S13=1475.5

Substitute in the sum formula:

S%5Bn%5D=expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29%5E%22%22d%29
S%5B13%5D=expr%2813%2F2%29%282a%5B1%5D%2B%2813-1%29%5E%22%22d%29
1475.5=expr%2813%2F2%29%282a%5B1%5D%2B%2812%29%5E%22%22d%29
Multiply both sides by 2:
2951=13%282a%5B1%5D%2B12d%29
Divide both sides by 13
227=2a%5B1%5D%2B12d

131 is known to be the 8th term. Find the first term and common difference of this sequence?
----
n=8, a8=131

Substitute in the nth term formula:

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d
a%5B8%5D=a%5B1%5D%2B%288-1%29%5E%22%22d%29
131=a%5B1%5D%2B7d%29

That gives us a system of two equations in two unknowns:

system%28227=2a%5B1%5D%2B12d%2C131=a%5B1%5D%2B7d%29

Solve that system by substitution or elimination and you'll
get the answer.  You do that by yourself.

Edwin