# Geometric series [easy]

• Aug 21st 2012, 01:37 AM
manoistheman
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):
Attachment 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.

• Aug 21st 2012, 01:40 AM
Prove It
Re: Geometric series [easy]
Quote:

Originally Posted by manoistheman
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):
Attachment 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.

Is this a geometric series or a geometric sequence?
• Aug 21st 2012, 01:45 AM
manoistheman
Re: Geometric series [easy]
Quote:

Originally Posted by Prove It
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.
• Aug 21st 2012, 01:55 AM
Prove It
Re: Geometric series [easy]
Quote:

Originally Posted by manoistheman
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):
Attachment 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.

\displaystyle \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.
• Aug 21st 2012, 02:05 AM
manoistheman
Re: Geometric series [easy]
Quote:

Originally Posted by Prove It
\displaystyle \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.