SOLUTION: In Arithmetic series, the 3rd term is twice the 8th term. Find the sum of the first 25 terms

Question 1067137: In Arithmetic series, the 3rd term is twice the 8th term. Find the sum of the first 25 terms
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The nth term of an arithmetic sequence is a(n) = a(1) + d(n-1), where a(1) is the first term and d is the common difference
:
a(3) = a(1) + d(3-1)
a(8) = a(1) + d(8-1)
:
We are given
:
a(1) + 2d = 2(a(1) + 7d)
:
a(1) + 2d = 2a(1) + 14d
:
a(1) + 12d = 0
:
a(1) = -12d
a(25) = a(1) + d(25-1)
:
The sum of the first n terms of an arithmetic sequence is S(n) = (n/2)(a(1) + a(n))
:
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S(25) = (25/2)(-12d + (-12d)+(24d)) = 0
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:

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