# arithmetic

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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 -

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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