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Math Help - Determine a

  1. #1
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    Determine a

    Determine a when : a+a*1.2+a*(1.2)^2+a*(1.2)^2+a*(1.2)^3+...+a*(1.2)^ 24=2000
    It's under mixed exercises in my book. But i can't find anything that looks like this in my book. I just can't find out what to do, so ended up trying to guess a and slove it. Anyone can give me a hint. I know it's probarbly very easy...
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  2. #2
    Super Member Matt Westwood's Avatar
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    Re: Determine a

    Quote Originally Posted by Portion View Post
    Determine a when : a+a*1.2+a*(1.2)^2+a*(1.2)^2+a*(1.2)^3+...+a*(1.2)^ 24=2000
    It's under mixed exercises in my book. But i can't find anything that looks like this in my book. I just can't find out what to do, so ended up trying to guess a and slove it. Anyone can give me a hint. I know it's probarbly very easy...
    Sum of a geometrical progression.

    Call the sum S, then multiply it by 1.2, then do 1.2 S - S and see what you get after simplifying.
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  3. #3
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    Re: Determine a

    Hello, Portion!

    \text{Determine }a\text{ when:}

    . . a+a(1.2)+a(1.2)^2+a(1.2)^2+a(1.2)^3+ \hdots +a(1.2)^{24} \:=\:2000

    Matt Westwood identitied the equation: the sum of a geometric sequence.

    The first term is: a.
    The common ratio is: r = 1.2
    And there are: n = 25 terms.


    The sum of the first n terms of a geometric sequence

    . . is given by: . S_n \;=\;a\,\frac{r^n-1}{r-1}


    So we have: . a\,\frac{1.2^{25} - 1}{1.2-1} \:=\:2000

    . . Solve for a.

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  4. #4
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    Re: Determine a

    a=2000*(1.2-1) / (1.2^25) -1 = 4.237457964
    ans * (1.2^25)-1 / 1.2-1 = 2000 ))) So happy now Thx!
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  5. #5
    Super Member Matt Westwood's Avatar
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    Re: Determine a

    Well yes okay, but my technique doesn't require you to learn a formula to plug numbers into, it teaches you why the formula works. Still, if it's just a formula for doing your maths homework you want, rather than understanding of why, then no worries.
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