# Thread: Finite geometric Series Problem

1. ## Finite geometric Series Problem

Hello i wondering if anyone could give me a hand solving this

Given
1. the sum of the geometric progression := S
2. the number of terms := n
3. the first term := t

Can you get an equation for the common ratio???

finite G.P S = t * ( 1 - r^n)/(1 - r)

the number i workin off are
S = 292.618
n = 15
t = 50

i dont know the sequence as i'm using this for a c++ program and numbers vary!
Anto!!!

2. Originally Posted by anthonycronin
Hello i wondering if anyone could give me a hand solving this

Given
1. the sum of the geometric progression := S
2. the number of terms := n
3. the first term := t

Can you get an equation for the common ratio???

finite G.P S = t * ( 1 - r^n)/(1 - r)

the number i workin off are
S = 292.618
n = 15
t = 50

i dont know the sequence as i'm using this for a c++ program and numbers vary!
Anto!!!
In the spirit of the challenge of finding the oldest unanswered post, this question is after a bit of jiggery pokery asking for solutions of:

$\displaystyle r^n-\frac{S}{t}r+\frac{S-t}{t}=0$

or rewritting this:

Can we find one or more real roots of:

$\displaystyle r^n-ar+b=0$

in closed form when $\displaystyle n>4$.

(The condition on $\displaystyle n$ is because we have the formulas for the roots for $\displaystyle n=1,\ 2,\ 3,\ 4$. Though something more elegant for the last two cases would be nice).

CB

3. Originally Posted by CaptainBlack
In the spirit of the challenge of finding the oldest unanswered post, this question is after a bit of jiggery pokery asking for solutions of:

$\displaystyle r^n-\frac{S}{t}r+\frac{S-t}{t}=0$

or rewritting this:

Can we find one or more real roots of:

$\displaystyle r^n-ar+b=0$

in closed form when $\displaystyle n>4$.

(The condition on $\displaystyle n$ is because we have the formulas for the roots for $\displaystyle n=1,\ 2,\ 3,\ 4$. Though something more elegant for the last two cases would be nice).

CB
I thought unanswered posts that old got deleted during the 'Great Purge' (it obviously wasn't in Urgent Help forum) ....