SOLUTION: In a sequence each even term is a times than the previous term and each odd term is c times than the previous term.The first term is 1. Find the sum of 2n terms.

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Question 1089825: In a sequence each even term is a times than the previous term and each odd term is c times than the previous term.The first term is 1. Find the sum of 2n terms.
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
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Separate the sum of 2n terms in two sums:

   First sum S1 consists of odd terms of the original sequence, and 

   second sum S2 consists of even terms.


Then the terms of S1 form geometric progression with the first term 1 and the common ratio of ac (= a*c).


The terms of S2 form geometric progression with the first term "a" and the common ratio of ac (= a*c).


Calculate the sums S1 and S2 using the common rule (formula) for geometric progression.


Then take the sum S1 + S2.

Solved.

When you complete your calculations, do not forget to send your "thanks" to me for clear instructions.


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There is a bunch of lessons on geometric progressions in this site
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
    - One characteristic property of geometric progressions
    - Solved problems on geometric progressions
    - Fresh, sweet and crispy problem on arithmetic and geometric progressions
    - Mathematical induction and geometric progressions
    - Mathematical induction for sequences other than arithmetic or geometric


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 "Geometric progressions".


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