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 Pre-Calculus and Calculus
 Geometric & arithmetic sequences... precalc help
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happysharlee
Junior Member

USA
5 Posts

Posted - 01/03/2011 :  19:25:50  Show Profile  Reply with Quote
Suppose that a, b, and c are three consecutive terms in a geometric sequence. Show that 1/(a+b) , 1/(2b) , and 1/(c+b) are three consecutive terms in an arithmetic sequence.

I have no clue how to approach this question! It's from my textbook, so i know all relevant equations/formulas. Please help me out, my teacher is very strict.


EDIT:
I have a second question:

Let b denote a positive constant. Find the sum of the first n terms in the sequence

1/(1+b) , 1/(1-b) , 1/(1-b) , ...

I get that the denominators must form some kind of arithmetic sequence, but I can't for the life of me figure out what the common difference could be... please help!!

Edited by - happysharlee on 01/03/2011 21:59:50
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Dr.Steve
New Member

USA
2 Posts

Posted - 01/04/2011 :  19:22:40  Show Profile  Reply with Quote
Since the sequence is geometric there is a common ratio r. Then b=ar and c= ar. See if you can take it from there.
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