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    1) A GP has a 1st term of 6 and a sum to infinity of 60. Find the common ratio.

    I've done
    S=\frac{a}{1-r}
    60=\frac{6}{1-r}
    \frac{60}{6}=1-r
    10=1-r
    9=-r
    r=-9

    The answer given in the book is 9/10.

    Am I using the right method? And if so, where have I gone wrong.


    2) Work out each of these sums
    \displaystyle\sum_{r=1}^{\infty} (0.3)^r+1

    I've got as far as
    a=(0.3)^2=0.9
    Unsure what r would equal though.


    Thanks.
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    (Original post by N!*)
    1) A GP has a 1st term of 6 and a sum to infinity of 60. Find the common ratio.

    I've done
    S=\frac{a}{1-r}
    60=\frac{6}{1-r}
    \frac{60}{6}=1-r
    10=1-r
    9=-r
    r=-9

    The answer given in the book is 9/10.

    Am I using the right method? And if so, where have I gone wrong.


    2) Work out each of these sums
    \displaystyle\sum_{r=1}^{\infty} (0.3)^r+1

    I've got as far as
    a=(0.3)^2=0.9
    Unsure what r would equal though.


    Thanks.
    60=\frac{6}{1-r}
    from here, multiply the denominator of 1-r to both sides.
    so, 60(1-r)=6, then expand and simplify.
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    (Original post by KeineHeldenMehr)
    60=\frac{6}{1-r}
    from here, multiply the denominator of 1-r to both sides.
    so, 60(1-r)=6, then expand and simplify.
    Thanks , thought it might be something like that.
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    (Original post by N!*)
    Thanks , thought it might be something like that.
    for the 2nd question
    calculate a again, i get 0.09
    the geometric progression works like this: a, ar, ar^2, ar^3

    so a=0.09, ar = 0.027 (by subbing into the summation formula given in the question.)

    divide ar by a to get the ratio.

    Spoiler:
    Show
    you should get r=0.3, then use the sum to infinity formula then hey presto!
    • Thread Starter
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    (Original post by KeineHeldenMehr)
    for the 2nd question
    calculate a again, i get 0.09
    the geometric progression works like this: a, ar, ar^2, ar^3

    so a=0.09, ar = 0.027 (by subbing into the summation formula given in the question.)

    divide ar by a to get the ratio.

    Spoiler:
    Show
    you should get r=0.3, then use the sum to infinity formula then hey presto!
    Such a great help, thankyou so much
    :adore: +rep
 
 
 
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Updated: February 13, 2010
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