SOLUTION: Find 'n' for an arithmetic sequence for which Sn= 345, a=12, and d=5.

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Question 859194: Find 'n' for an arithmetic sequence for which Sn= 345, a=12, and d=5.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

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

S%5Bn%5D=+%28n%2F2%29%2824+%2B+%28n-1%295%29+=+345

          n(19 + 5n) = 690

          5n^2 + 19n - 690 = 0

n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ 

n+=+%28-19+%2B-+sqrt%28+14161+%29%29%2F%2810%29+ Tossing out negative solution

n+=+%28-19+%2B-+119%29%2F%2810%29+

      n = 10