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Math Help - nth partial sum of a geometric sequence

  1. #1
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    nth partial sum of a geometric sequence

    I don't even know if this is an nth partial sum of a geometric sequence problem but...
    if someone wanted to save money to buy a used car and they saved $100 on the first day, then $75 on the second day, then $56.25 on the third day, how much will they have saved on the seventh day?
    In 20 days, will they have enough to afford a used car that costs $500?
    what would be the total amount they saved in that time?

    thanks
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Intsecxtanx View Post
    I don't even know if this is an nth partial sum of a geometric sequence problem but...
    if someone wanted to save money to buy a used car and they saved $100 on the first day, then $75 on the second day, then $56.25 on the third day, how much will they have saved on the seventh day?
    In 20 days, will they have enough to afford a used car that costs $500?
    what would be the total amount they saved in that time?

    thanks
    HI

    This is a geometric sequence with a=100 , and r =0.75

    On the 7th day , they will save T_7=ar^{n-1}=100(0.75)^{7-1}

    In 20days , they would have saved (in total)

    S_20=\frac{100(1-0.75^{20})}{1-0.75}

    Calculate this and if see whther its > or < 500 .
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