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
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