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

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Question 141061: The 12th term of an arithmetic series is 42 and the sum of the first 17 terms is 51. Find the common difference of the series, and find the first three terms of the series.
Answer by stanbon(75887) About Me  (Show Source):
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The 12th term of an arithmetic series is 42 and the sum of the first 17 terms is 51. Find the common difference of the series, and find the first three terms of the series.
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a(12) = a(1) + 11d = 42
S(17) = 17(a(1) + {a(1)+16d))/2 = (34a(1) 272d)/2 = 17a(1) + 136d = 51
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Rearrange:
a(1) + 11d = 42
17a(1) + 136d = 51
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Multiply thru 1st equation by 17 to get:
17a(1) + 187d = 714
17a(1) + 136d = 51
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Subtract 2nd from 1st to get:
51d = 663
d = 13
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Substitute into a(1) + 11d = 42 to solve for a(1)
a(1) + 143= 42
a(1) = -101
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Cheers,
Stan H.