Posted by **Ashley** on Tuesday, December 27, 2011 at 9:13pm.

The sum of the first 4 terms of an arithmetic series is -8 and the sum of the first 5 terms is 85. Determine the first term and the common difference

- arithmetic -
**Reiny**, Tuesday, December 27, 2011 at 10:51pm
So Sum(5) - Sum(4) = term(5)

85-(-8) = a + 4d

a+4d = 93 < (#1)

Sum(4) = -8 , since there are only 4 terms I will not use the sum formula

a + a+d + a+2d + a+3d = -8

4a + 6d = -8

2a + 3d = -4 , (#2)

2(#1) - (#2) ---> 5d = 190

d = 38

in #1, a = -59

check:

-59 - 21 + 17+ 55 = -8

sum(5) = sum(4) + term(5) = -8 + (-59+4(38)) = 85

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