SOLUTION: The fifth term of a geometric progression is 1 and the common ratio is ½. Find the eight term and an expression for the nth term.

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Question 1202405: The fifth term of a geometric progression is 1 and the common ratio is ½. Find the eight term and an expression for the nth term.
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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The fifth term of a geometric progression is 1 and the common ratio is ½.
Find (a) the highlight%28cross%28eight%29%29 eighth term and (b) an expression for the nth term.
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(a)  The 8-th term is  a%5B8%5D = a%5B5%5D%2A%281%2F2%29%5E3 = 1%2F8.     ANSWER


     The 1-st term is  a%5B1%5D = a%5B5%5D%2A%281%2F2%29%5E%28-4%29 = 2%5E4 = 16.


(b)  The n-th term is  a%5Bn%5D = a%5B1%5D%2A%281%2F2%29%5E%28n-1%29 = 16%2F2%5E%28n-1%29 = 2%5E%285-n%29 = 2%5E5%2F2%5En = 1%2F2%5E%28n-5%29.    ANSWER


For (b), you can take any of these four last equivalent expressions.

Solved.

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On geometric progressions,  see introductory lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
in this site.

Learn the subject from there.