SOLUTION: The sum of 6 terms of an arithmetic series is 45, the sum of 12 terms is -18. Find the first term and the common difference.
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Question 512217: The sum of 6 terms of an arithmetic series is 45, the sum of 12 terms is -18. Find the first term and the common difference. Answer by Edwin McCravy(20056) (Show Source):
You can put this solution on YOUR website! The sum of 6 terms of an arithmetic series is 45, the sum of 12 terms is -18. Find the first term and the common difference.
Sn = [2a1 + (n-1)d]
S6 = [2a1 + (6-1)d]
45 = 3[2a1 + 5d]
15 = 2a1 + 5d
2a1 + 5d = 15
S12 = [2a1 + (12-1)d]
-18 = 6[2a1 + 11d]
-3 = 2a1 + 11d
2a1 + 11d = -3
So we have the system of equations
2a1 + 5d = 15
2a1 + 11d = -3
Solve that system either by substitution or elimination and
get a1 = 15, d = -3
Edwin
