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Math Help - Geometric series [easy]

  1. #1
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    Geometric series [easy]

    Hey guys,

    Just wondering if anybody could help me identify the r value in the following geometric series (sorry it's in image form, I'm no good at tex):
    Geometric series [easy]-series.png
    Anyway, I had one similar just before where the coefficient was 1, meaning my a and r terms were both x - which made it easy - but this is for an extra little part on an assignment and I haven't done APs and GPs in about a year so I need a little refresh.

    Thanks in advance.
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  2. #2
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    Re: Geometric series [easy]

    Quote Originally Posted by manoistheman View Post
    Hey guys,

    Just wondering if anybody could help me identify the r value in the following geometric series (sorry it's in image form, I'm no good at tex):
    Click image for larger version. 

Name:	series.PNG 
Views:	2 
Size:	2.4 KB 
ID:	24566
    Anyway, I had one similar just before where the coefficient was 1, meaning my a and r terms were both x - which made it easy - but this is for an extra little part on an assignment and I haven't done APs and GPs in about a year so I need a little refresh.

    Thanks in advance.
    Is this a geometric series or a geometric sequence?
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    Re: Geometric series [easy]

    Quote Originally Posted by Prove It View Post
    Is this a geometric series or a geometric sequence?
    Series - I will be using the a and r values to calculate the sum to infinity.

    Thanks for the speedy reply by the way.
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  4. #4
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    Re: Geometric series [easy]

    Quote Originally Posted by manoistheman View Post
    Hey guys,

    Just wondering if anybody could help me identify the r value in the following geometric series (sorry it's in image form, I'm no good at tex):
    Click image for larger version. 

Name:	series.PNG 
Views:	2 
Size:	2.4 KB 
ID:	24566
    Anyway, I had one similar just before where the coefficient was 1, meaning my a and r terms were both x - which made it easy - but this is for an extra little part on an assignment and I haven't done APs and GPs in about a year so I need a little refresh.

    Thanks in advance.
    \displaystyle \begin{align*} a &= S_1 \\  \\ a + r\,a &= S_2 \\ x + r\,x &= 1.6x + 1.6x^2 \\ \\ a + r\,a + r^2a &= S_3 \\ x + r\,x + r^2x &= 1.6x + 1.6x^2 + x^3 \end{align*}

    You should be able to solve for r now.
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  5. #5
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    Re: Geometric series [easy]

    Quote Originally Posted by Prove It View Post
    \displaystyle \begin{align*} a &= S_1 \\  \\ a + r\,a &= S_2 \\ x + r\,x &= 1.6x + 1.6x^2 \\ \\ a + r\,a + r^2a &= S_3 \\ x + r\,x + r^2x &= 1.6x + 1.6x^2 + x^3 \end{align*}

    You should be able to solve for r now.
    Oh my god, a=1.6x and r=x - just subbed in the values into the sum to infinity and got it right!
    Thank you good sir, though I feel silly for not seeing this earlier haha.

    EDIT: Actually, I apologise; the initial value I had listed as x SHOULD have been 1.6x - that would've made it a whole lot simpler in terms of the a value. Silly mistake on my part, and thanks for the help; I guess that's what tripped me up.
    Last edited by manoistheman; August 21st 2012 at 02:12 AM.
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