SOLUTION: the 3rd term of a linear sequence is twice the 1st term and the 8th term of the sequence is four more than the 6th term. find the first term of the arithmetic progression.

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Question 1085662: the 3rd term of a linear sequence is twice the 1st term and the 8th term of the sequence is four more than the 6th term. find the first term of the arithmetic progression.
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
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Since "the 8th term of the sequence is four more than the 6th term", it implies that the common difference is half of 4, i.e. d = 2.


Since "the 3rd term of a linear sequence is twice the 1st term", it means that

 = ,   or

 = .


Hence,  = 4.


Thus the first term of the AP is 4 and the common difference is 2.

Solved.

Notice that the term "linear sequence" is out of use. The canonical term is Arithmetic progression on Arithmetic sequence.


On arithmetic progressions, see the lessons in this site:
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".



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