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Math Help - 2 questions on geometric sequences

  1. #1
    Member M670's Avatar
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    2 questions on geometric sequences

    For each sequence, find a formula for the general term, . For example, answer if given the sequence:

    1. really to sure about this one
    2. in this one I see the pattern that 1/4 is half of 1/2 and 1/8 is half of 1/4 and 1/16 is half of 1/18 but I just can't seem to figure out the formula to show this


    And the next question is
    For the sequence
    its fifth partial sum .
    its th partial sum .

    Any explanation into what exactly is being asked would be great I went back to my chapter twice and still can't figure out the partial sum part of sequeneces
    Thanks Guys
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  2. #2
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    Re: 2 questions on geometric sequences

    1. This isn't a geometric sequence. You can factorise out 1/2 so that it becomes
    \frac{1}{2} (\frac{1}{1}, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, ... )

    2. This one is a geometric sequence.

    The general form for a geometric sequence is a_n = ar^{n-1}
    Where a is the first term and r is the common ratio

    Each term is half of the previous so the common ratio is 1/2, and the first term is 1/2.


    3. Find the first term a1
    Find the common ratio which is \frac{a_{n+1}}{a_n} for all values of n

    The fifth partial sum is a_1+a_2+a_3+a_4+a_5
    Likewise, the nth partial sum is a_1+a_2+a_3+...+a_n

    The sum of the first n terms is equal to a\frac{1-r^n}{1-r}
    To find the fifth partial sum you could find the first 5 terms and add them up, or use that formula.
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  3. #3
    Member M670's Avatar
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    Re: 2 questions on geometric sequences

    So then for #1 an=1(1/2)(n-1) and #2 an=(1/2)(1/2)(n-1)
    Now for the second question a1=3/31 does this make sense or am I way off?
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    Re: 2 questions on geometric sequences

    Quote Originally Posted by M670 View Post
    So then for #1 an=1(1/2)(n-1) and #2 an=(1/2)(1/2)(n-1)
    which is equal to 1/2n.

    Now for the second question a1=3/31 does this make sense or am I way off?
    Yes, the first term of (3/3n) is 3/3= 1. Now can you answer the last two questions?
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    Member M670's Avatar
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    Re: 2 questions on geometric sequences

    Quote Originally Posted by HallsofIvy View Post
    which is equal to 1/2n.


    Yes, the first term of (3/3n) is 3/3= 1. Now can you answer the last two questions?
    The first two I am confused with (1/2)^n
    And the second part I have S5=1.4814 or is it .01234567
    Then Sn=not sure.?
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