SOLUTION: the 12th term of an arithmatic series is 42 and the sum of the first 17 terms is 51. find the common difference of the series and the first three terms.

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Question 7015: the 12th term of an arithmatic series is 42 and the sum of the first 17 terms is 51. find the common difference of the series and the first three terms.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
12th term is a+11d = 42 --eqn1.

Formula for summation is S%5Bn%5D = %28n%2F2%29%282a+%2B+%28n-i%29d%29, so as S%5B17%5D = 51 we get:

S%5B17%5D = %2817%2F2%29%282a+%2B+%2817-i%29d%29 = 51

%2817%2F2%29%282a+%2B+16d%29+=+51
2a+%2B+16d+=+6
--> a+8d = 3 --eqn2

Solve eqn1 and 2 simultaneously to get a and d. -101 and 13

jon.