# arithmetic

If the sum is 220 and the first term is 10, find the common difference if the last term is 30

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1. Since you are using the term "common difference" I must assume you are dealing with an arithmetic series.

a = 10
t(n) = 30
t(n) = a+(n-1)d
30 = 10 + (n-1)d
20 = (n-1)d , ( #1)

S(n) = (n/2)(first + last)
220 = (n/2)(40)
20n = 220
n = 11

back in #1:
20 = 10d
d = 2

check:
term(11) = a+ 10d = 10 + 2(11-1) = 30
sum(11) = (11/2)(10+30) = 220

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posted by Reiny

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