SOLUTION: the sum of the first two terms of an arithmetic sequence is 16, and the sum of the second and third term is 28, determine the first three terms

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Question 880739: the sum of the first two terms of an arithmetic sequence is 16, and the sum of the second and third term is 28, determine the first three terms
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
General term, a%2B%28n-1%29d. First term is a. Common difference is d. n is the index of any term.

First Two Terms Sum:
a%2B%281-1%29d%2Ba%2B%282-1%29d=16
a%2Ba%2Bd=16
highlight_green%282a%2Bd=16%29

Second and Third Terms Sum:
a%2B%282-1%29d%2Ba%2B%283-1%29d=28
a%2Bd%2Ba%2B2d=28
highlight_green%282a%2B3d=28%29

Starting with Elimination Method would be best because both equations have a 2a term.
%282a%2B3d%29-%282a%2Bd%29=28-16
2d=12
d=6
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The simplified term one and two sum equation can be chosen for finding a.
2a%2Bd=16
2a=16-d
a=%2816-d%29%2F2
Substitute for d:
a=%2816-6%29%2F2
a=5
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The general term is now more specifically, highlight%285%2B%28n-1%29%2A6%29.
First three terms: 5, 11, 16.