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Math Help - Infinite geometric sequence question

  1. #1
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    Infinite geometric sequence question

    The second term of an infinite geometric sequence is 4/9, and the sixth term is 9/64.

    What is the sum of the first five terms of this sequence?

    What is the sum of all off the terms of this sequence?
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  2. #2
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    Hello,
    Quote Originally Posted by cityismine View Post
    The second term of an infinite geometric sequence is 4/9, and the sixth term is 9/64.

    a_2=4/9
    a_6=9/64

    we also know that a_6=a_2*q^4, where q is the constant progression.

    Then a_6/a_2=81/256=q^4 and :


    q=+ or - 3/4

    Is it enough for you to continue ? (there are 2 possible answers to the following questions ^^)
    Last edited by Moo; July 26th 2008 at 02:14 AM. Reason: pictures have disappeared
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  3. #3
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    Also, you're probably gonna need this:
    Sum of a geometric series:


    Sum of an infinite geometric series:


    Also, to find t_1, just remember that:


    Like, for instance:
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  4. #4
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    Thanks, I was able to take it from there and solve it. The answers I got are 781/432 and 27/64. They match the ones in the back of the book.
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