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Thread: infinite geometric series

  1. #1
    Super Member bigwave's Avatar
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    Cool infinite geometric series

    the sum of an infinite geometric series with first term a and common ratio r < 1 is given by.

    $\displaystyle \frac{a}{1-r}$

    The sum of a given infinite geometric series is $\displaystyle 200$, and the common ratio is$\displaystyle 0.15.$

    What is the second term of this series?

    by pluging the info given i got for an a value of $\displaystyle a=170$ which is not the value of the second term but that is where i don't understand how you find out what the second term is.

    if

    $\displaystyle \frac{a}{1-0.15} = 200$

    then

    $\displaystyle a=170$

    the ans for the second term is $\displaystyle 25.5$ how did they get this. I looked at examples from several books but still ?

    thnx ahead for help
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Re: infinite geometric series

    Quote Originally Posted by bigwave View Post
    the sum of an infinite geometric series with first term a and common ratio r < 1 is given by.

    $\displaystyle \frac{a}{1-r}$

    The sum of a given infinite geometric series is $\displaystyle 200$, and the common ratio is$\displaystyle 0.15.$

    What is the second term of this series?

    by pluging the info given i got for an a value of $\displaystyle a=170$ which is not the value of the second term but that is where i don't understand how you find out what the second term is.

    if

    $\displaystyle \frac{a}{1-0.15} = 200$

    then

    $\displaystyle a=170$

    the ans for the second term is $\displaystyle 25.5$ how did they get this. I looked at examples from several books but still ?

    thnx ahead for help
    for any geometic series ...

    $\displaystyle a_{n+1} = a_n \cdot r$

    $\displaystyle a_2 = a_1 \cdot r = 170 \cdot 0.15 = 25.5$
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