SOLUTION: the sum of the first twelve terms of an arithmetic sequence is 1188. if the sixth term is 89, find the first term, the common difference and the fifteenth term

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Question 1083084: the sum of the first twelve terms of an arithmetic sequence is 1188. if the sixth term is 89, find the first term, the common difference and the fifteenth term
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
d, common difference
a%5B1%5D, first term of sequence

%2812%2F2%29%28a%5B1%5D%2B%2812-1%29d%29=1188
6%28a%5B1%5D%2B11d%29=1188
a%5B1%5D%2B11d=198

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a%5B6%5D=a%5B1%5D%2B%286-1%29d=89
a%5B1%5D%2B5d=89

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System of equations in the unknown variables a%5B1%5D and d:
system%28a%5B1%5D%2B11d=198%2Ca%5B1%5D%2B5d=89%29
Solve the system for the unknown variables.