Question 942261: In an arithmetic series, how can I find the value of the first term, given the 14th term equals 200 and the sum of the first 20 terms equals 3230.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In an arithmetic series, how can I find the value of the first term, given the 14th term equals 200 and the sum of the first 20 terms equals 3230.
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a(14) = a(1) + 13d = 200
3230 = (20/2)(a(1)+a(20))
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Rearrange::
a(1) + 13d = 200
a(1) + a(20) = 323
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a(20)- 13d = 123
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Note:: a(20) = a(14)+6d = 200 + 6d
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So, 200+6d - 13d = 123
-7d = -77
d = 11
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Solve for a(1)::
a(14) = a(1) + 13d = 200
a(1) = 200-13*11
a(1) = 200-143
a(1) = 57
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Cheers,
Stan H.
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