SOLUTION: The first term of an arithmetic progression is 8 and the last term is 34. The sum of the first six terms is 58. Find the number of terms in this progression.

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Question 1186959: The first term of an arithmetic progression is 8 and the last term is 34. The sum of the
first six terms is 58. Find the number of terms in this progression.
Answer by MathLover1(20849) About Me  (Show Source):
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a%5B1%5D=8
a%5Bn%5D=34
The sum of the first six terms is 58.

Sum of the first six terms:
%286%2F2%29%282%2A8%2B5%2Ad%29=58
3%2816%2B5d%29=58
48%2B15d=58
15d=10
d=2%2F3
plug it in last term formula and solve for n:
34=8%2B%28n-1%29d
26=%28n-1%29%282%2F3%29
39=n-1
+n=40