How to solve/simplify (1/4)^n-1?

**benny92000** · July 28th 2011, 07:13 PM

The problem is as follows:

1/4=64(1/4)^n-1

The answer is 5...

(I am working with Arithmetic Sequences.)

**Siron** · July 28th 2011, 07:32 PM

So you have the equation:
$\frac{1}{4}=64\cdot \left(\frac{1}{4}\right)^{n-1}$
Write the equation as:
$\frac{1}{4}=\left(\frac{1}{4}\right)^{-3}\cdot \left(\frac{1}{4}\right)^{n-1}$
$\Leftrightarrow \frac{1}{4}$ $= \left(\frac{1}{4}\right)^{n-4}$

...

**benny92000** · July 28th 2011, 08:12 PM

Originally Posted by Siron

So you have the equation:
$\frac{1}{4}=64\cdot \left(\frac{1}{4}\right)^{n-1}$
Write the equation as:
$\frac{1}{4}=\left(\frac{1}{4}\right)^{-3}\cdot \left(\frac{1}{4}\right)^{n-1}$
$\Leftrightarrow \frac{1}{4}$ $= \left(\frac{1}{4}\right)^{n-4}$

...

Thank you. You're the man.

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