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Math Help - Geometric sequence

  1. #1
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    Geometric sequence

    Write the expression for the nth term of the geometric sequence. Then find the 20th term of the sequence.

    a1= 100, r= 1.05
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  2. #2
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    Hi thepride

    Do you know the general fomula for the nth term of the geometric sequence?
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  3. #3
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    Quote Originally Posted by thepride View Post
    Write the expression for the nth term of the geometric sequence. Then find the 20th term of the sequence.

    a1= 100, r= 1.05
     100 * 1.05^n

     100 * 1.05^20 = 265.3297705

    Therefore the 20th term is 265.3297705

    Note. The 1.05^20 means 1.05 times itself 20 times.
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  4. #4
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    Quote Originally Posted by Barthayn View Post
     100 * 1.05^n

     100 * 1.05^20 = 265.3297705

    Therefore the 20th term is 265.3297705

    Note. The 1.05^20 means 1.05 times itself 20 times.
    i dont think that is right barthayn. its more like an= 100(1.05)^n-1 which is about 252.695
    ?
    im not sure though can someone check my work?
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  5. #5
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    Quote Originally Posted by thepride View Post
    i dont think that is right barthayn. its more like an= 100(1.05)^n-1 which is about 252.695
    ?
    im not sure though can someone check my work?

    HI

    indeed

     <br />
T_20=100(1.05)^{19}<br />
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  6. #6
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    Quote Originally Posted by thepride View Post
    i dont think that is right barthayn. its more like an= 100(1.05)^n-1 which is about 252.695
    ?
    im not sure though can someone check my work?
    well if you look the formula is An= A1*1.05^n-1
    so you would plug in An= 100*1.05^(20-1) which is the given answer in your book.
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  7. #7
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    yeah, Flexus is right, I forgot to subtract n by one. You have to n-1 because 1.05 counts for the first one.
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