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

• May 24th 2007, 05:44 PM
stlawrenceriver
rewriting a geometric sequence formula to solve for 'n'
The question is...
Rewrite the equation tn=ar^n-1 to solve for 'n'
• May 24th 2007, 05:47 PM
ThePerfectHacker
Quote:

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

What is $t_n$?
• May 24th 2007, 05:50 PM
stlawrenceriver
that's the problem, there is no value for tn
• May 24th 2007, 05:54 PM
Jhevon
Quote:

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

$t_n = ar^{n - 1}$

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

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

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

$\Rightarrow n = \frac {ln \left( \frac {t_n}{a} \right) }{ln(r)} + 1$
• May 24th 2007, 05:56 PM
Jhevon
Quote:

Originally Posted by ThePerfectHacker
What is $t_n$?

i think $t_n$ just represents any arbitrary term of the geometric sequence $\left ( t_n \right)$
• May 24th 2007, 06:34 PM
stlawrenceriver
Thank you so much for the help, now I know what I'm doing.:)