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(52788) (Show Source):
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.
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