SOLUTION: Find a(1) for the arithmetic series with S(7) = 287 and d = 12. I know the answer is 5, but don't know the formula for solving the problem.

Algebra ->  Sequences-and-series -> SOLUTION: Find a(1) for the arithmetic series with S(7) = 287 and d = 12. I know the answer is 5, but don't know the formula for solving the problem.      Log On


   

Question 374462: Find a(1) for the arithmetic series with S(7) = 287 and d = 12. I know the answer is 5, but don't know the formula for solving the problem.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

for an arithmetic series: S%5Bn%5D=%28n%2F2%29%282%2Aa%5B1%5D%2B+%28n-1%29d%29

In this series d = 12

S%5Bn%5D=%28n%2F2%29%282%2Aa%5B1%5D%2B+%28n-1%2912%29

question states:

S%5B7%5D=%287%2F2%29%282%2Aa%5B1%5D%2B+%286%29%2A12%29=+287

%287%2F2%292%2Aa%5B1%5D%2B+%287%2F2%29%286%29%2A12=+287

7%2Aa%5B1%5D%2B+252+=+287

  7* a[1] = 287-252  

  7* a[1] = 35

     a[1] = 5