# Math Help - Annuities and Geometric Series

1. ## Annuities and Geometric Series

Okay so I understand how to do these questions when I have the last term. But I do not know how to find n when I only have the first three terms. Here's an example:

S10 in the series $2500 +$2562.50 + %2626.56 + ...

so am I still supposed to use the formula tn=ar^n-1?

if so how do i find the tn?

2. Originally Posted by VDestinV
Okay so I understand how to do these questions when I have the last term. But I do not know how to find n when I only have the first three terms. Here's an example:

S10 in the series $2500 +$2562.50 + %2626.56 + ...

so am I still supposed to use the formula tn=ar^n-1?

if so how do i find the tn?
Well for S10, n would be 10, r would be (2562.2/2500) and a would be 2500.

3. Originally Posted by sean.1986
Well for S10, n would be 10, r would be (2562.2/2500) and a would be 2500.
but like in this:
tn= ar^n-1
640 = 5(2)^n-1
128 = (2)^n-1
(2)^7=(2)n-1
7=n-1
n=8

I wanna be able to do that but I can not because I do not know what tn equals.

4. Isn't Tn just the nth term for an arbitrary n? Which term are you trying to find?

5. Originally Posted by sean.1986
Isn't Tn just the nth term for an arbitrary n? Which term are you trying to find?
I'm actually trying to find the sum but first I have to find n, n is the term number whereas tn is the actual amount. I'm trying to find t i guess

6. Why don't you use the formula for the sum?

$Sn = \frac{a(1 - r^n)}{1-r}$

7. Originally Posted by sean.1986
Why don't you use the formula for the sum?

$Sn = \frac{a(1 - r^n)}{1-r}$
because I need to know n

8. So you know the nth term but not what n is? What's the nth term?

9. Originally Posted by sean.1986
So you know the nth term but not what n is? What's the nth term?
10 i think

10. That would be n, not the nth term.

If you're looking for the 10th term, then...

$r = \frac{2562.5}{2500}$

$a10 = 2500r^9$

11. look im sorry but you are confusing me.