The sum of the first 4 terms of an arithmetic series is -8 and the sum of the first 5 terms is 85...?
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Answer:
The sum of the first n terms of the series with starting value "a" and common difference "d" is .. s(n) = n*a + n(n-1)/2*d The 4th and 5th terms are thus .. s(4) = 4a + 6d .. s(5) = 5a + 10d Using Cramer's rule, we can find .. a = (10s(4) - 6s(5))/(4*10 - 5*6) = s(4) - 0.6s(5) = -8 - 0.6*85 = -59 .. d = (4s(5) - 5s(4))/10 = 0.4s(5) - s(4)/2 = 0.4*85 - (-8)/2 = 38 The first term is -59, and the common difference is 38. <=== ANSWER _____ The first 5 terms of the series are -59, -21, 17, 55, 93.
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The sum of the first n terms of the series with starting value "a" and common difference "d" is .. s(n) = n*a + n(n-1)/2*d The 4th and 5th terms are thus .. s(4) = 4a + 6d .. s(5) = 5a + 10d Using Cramer's rule, we can find .. a = (10s(4) - 6s(5))/(4*10 - 5*6) = s(4) - 0.6s(5) = -8 - 0.6*85 = -59 .. d = (4s(5) - 5s(4))/10 = 0.4s(5) - s(4)/2 = 0.4*85 - (-8)/2 = 38 The first term is -59, and the common difference is 38. <=== ANSWER _____ The first 5 terms of the series are -59, -21, 17, 55, 93.
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