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Math Help - geometric sequences

  1. #1
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    geometric sequences

    Given the following geometric sequence: 32, ____, ____,4,.........

    Find the missing two terms




    find the nth term





    find the sum of the first 5 terms




    find the sum of all the terms. Explain your answer
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Airjunkie View Post
    Given the following geometric sequence: 32, ____, ____,4,.........

    Find the missing two terms




    find the nth term





    find the sum of the first 5 terms




    find the sum of all the terms. Explain your answer
    Examine a_n=32\bigg(\frac{1}{2}\bigg)^{n}
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  3. #3
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    so i solve that by plugging in 2, 3, and 5 in for n? That would give me the first 5 numbers.
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Airjunkie View Post
    so i solve that by plugging in 2, 3, and 5 in for n? That would give me the first 5 numbers.
    Yes...the corresponding natrual number you put in will yield the n-th term
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  5. #5
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    I have no idea what im doing.
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Airjunkie View Post
    I have no idea what im doing.
    Explain what you would do? Give me any inkling you have?
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  7. #7
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    I dont know,

    I thought i could do


    Gn = G1 * r^n-1

    I need some help bad.
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  8. #8
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Airjunkie View Post
    I dont know,

    I thought i could do


    Gn = G1 * r^n-1

    I need some help bad.
    Do you agree that this is the correct sequence? and yes that is the value for the sum of a geometric series
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  9. #9
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    No answers eh? Well shoot, if anyone can help me ill try to check this later tonight, maybe i can sneak into the library b4 math.

    Thanks,

    Airjunkie
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  10. #10
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    Quote Originally Posted by Airjunkie View Post
    Given the following geometric sequence: 32, ____, ____,4,.........

    Find the missing two terms


    find the nth term


    find the sum of the first 5 terms


    find the sum of all the terms. Explain your answer
    Ok based on the given we can observe that the sequence is decreasing by n(1/2). That gives us the complete sequence: 32,16,8,4.
    There is a formula for this but it requires two consecutive numbers in a series which is rn=an / an-1

    the nth term can be calculated by the formula an=a1r^n-1. We already determined that r=1/2 above. So we just need to plug in our values
    an=32* (1/2)^n-1. We can now use this formula to calculate any of the n terms we would like.

    Sum of the first 5 terms is done by the formula: Sn=a1 (1-r^n)/1-r
    So we plug in our Values:
    S5=32(1-1/2^5)/1-1/2 >> S5=32(1-1/32)/.5 >> S5=32(31/32)/.5 S5 = 62

    For the last part we use the formula: Sinfinity= a1 /1-r
    this formula has a condition though the conditions are "r" must be between -1 & 1 for it to have an infinite series. Since our "r" value was 1/2 we are able to use this.

    Sinfinity= 32/1-.5 = 32/.5 = 64

    Hope this helps
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