# Thread: rewriting a geometric sequence formula to solve for 'n'

1. ## rewriting a geometric sequence formula to solve for 'n'

The question is...
Rewrite the equation tn=ar^n-1 to solve for 'n'

2. Originally Posted by stlawrenceriver
The question is...
Rewrite the equation tn=ar^n-1 to solve for 'n'
What is $\displaystyle t_n$?

3. that's the problem, there is no value for tn

4. Originally Posted by stlawrenceriver
The question is...
Rewrite the equation tn=ar^n-1 to solve for 'n'
$\displaystyle t_n = ar^{n - 1}$

$\displaystyle \Rightarrow r^{n - 1} = \frac {t_n}{a}$

$\displaystyle \Rightarrow ln \left( r^{n - 1} \right) = ln \left( \frac {t_n}{a} \right)$

$\displaystyle \Rightarrow (n - 1) ln(r) = ln \left( \frac {t_n}{a} \right)$

$\displaystyle \Rightarrow n = \frac {ln \left( \frac {t_n}{a} \right) }{ln(r)} + 1$

5. Originally Posted by ThePerfectHacker
What is $\displaystyle t_n$?
i think $\displaystyle t_n$ just represents any arbitrary term of the geometric sequence $\displaystyle \left ( t_n \right)$

6. Thank you so much for the help, now I know what I'm doing.