SOLUTION: In an arithmetic sequence of positive numbers, the common difference is twice the first term, and the sum of the first six terms is equal to the square of the first term. Find the

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Question 258336: In an arithmetic sequence of positive numbers, the common difference is twice the first term, and the sum of the first six terms is equal to the square of the first term. Find the first term of the sequence.
Answer by palanisamy(496) About Me  (Show Source):
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Let the first term of an arithmetic sequence be a.
Given,the common difference is twice the first term.
So the common difference d = 2a
Also, the sum of the first six terms is equal to the square of the first term.
(6/2)(a+a+5d) = a^2
3(2a+5*2a) = a^2
3(12a)=a^2
36a-a^2=0
a(36-a) = 0
a=0 or a=36
Therefore the first term is 36