# arithmetic

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the sum of the first 8 term of an arithmetic progresion is 220,if the third term is 17.Find the sum of the first 6 items

• arithmetic -

the third term is 17 ---> a+2d = 17
a = 17-2d

sum of first 8 terms = 220
---> (8/2)(2a + 7d) = 220
4(2a + 7d) = 220
2a + 7d = 55
2(17-2d) + 7d = 55
34 - 4d + 7d = 55
3d = 21
d = 7
then a = 3

sum(6) = 3(6 + 35) = 123

check:
terms are: 3 10 17 24 31 38 45 52 ..
sum(8) = 220
sum(6) = 123
all is good

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