rewriting a geometric sequence formula to solve for 'n'

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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.:)

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