Algebra Examples

$a_{n} = \frac{2}{5} {(5)}^{n - 1}$

Step 1

Remove parentheses.

$a_{n} = \frac{2}{5} \cdot 5^{n - 1}$

Step 2

Simplify $\frac{2}{5} \cdot 5^{n - 1}$ .

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Step 2.1

Combine $\frac{2}{5}$ and $5^{n - 1}$ .

$a_{n} = \frac{2 \cdot 5^{n - 1}}{5}$

Step 2.2

Cancel the common factor of $5^{n - 1}$ and $5$ .

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Step 2.2.1

Factor $5$ out of $2 \cdot 5^{n - 1}$ .

$a_{n} = \frac{5 (2 \cdot 5^{n - 2})}{5}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $5$ out of $5$ .

$a_{n} = \frac{5 (2 \cdot 5^{n - 2})}{5 (1)}$

Step 2.2.2.2

Cancel the common factor.

$a_{n} = \frac{5 (2 \cdot 5^{n - 2})}{5 \cdot 1}$

Step 2.2.2.3

Rewrite the expression.

$a_{n} = \frac{2 \cdot 5^{n - 2}}{1}$

Step 2.2.2.4

Divide $2 \cdot 5^{n - 2}$ by $1$ .

$a_{n} = 2 \cdot 5^{n - 2}$

Step 3

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.

$f (n) = 2 \cdot 5^{n - 2}$