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.

Thanks in advance.

Is this a geometric series or a geometric sequence?

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.

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.

Thanks in advance.

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

You should be able to solve for r now.

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.