Algebra Examples

$a_{n} = - 1 {(\frac{1}{3})}^{n - 1}$

Step 1

Simplify $- 1 {(\frac{1}{3})}^{n - 1}$ .

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Step 1.1

Apply the product rule to $\frac{1}{3}$ .

$a_{n} = - 1 \frac{1^{n - 1}}{3^{n - 1}}$

Step 1.2

One to any power is one.

$a_{n} = - 1 \frac{1}{3^{n - 1}}$

Step 1.3

Rewrite $- 1 \frac{1}{3^{n - 1}}$ as $- \frac{1}{3^{n - 1}}$ .

$a_{n} = - \frac{1}{3^{n - 1}}$

Step 2

To rewrite as a function of $n$ , write the equation so that $a_{n}$ is by itself on one side of the equal sign and an expression involving only $n$ is on the other side.

$f (n) = - \frac{1}{3^{n - 1}}$