Algebra Examples

$a_{n} = 2 \cdot {(\frac{1}{4})}^{n - 1}$

Step 1

Substitute in the value of $n$ to find the $n$ th term.

$a_{3} = 2 \cdot {(\frac{1}{4})}^{(3) - 1}$

Step 2

Simplify the expression.

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Step 2.1

Subtract $1$ from $3$ .

$a_{3} = 2 \cdot {(\frac{1}{4})}^{2}$

Step 2.2

Apply the product rule to $\frac{1}{4}$ .

$a_{3} = 2 \cdot \frac{1^{2}}{4^{2}}$

Step 2.3

One to any power is one.

$a_{3} = 2 \cdot \frac{1}{4^{2}}$

Step 2.4

Raise $4$ to the power of $2$ .

$a_{3} = 2 \cdot \frac{1}{16}$

$a_{3} = 2 \cdot \frac{1}{16}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $16$ .

$a_{3} = 2 \cdot \frac{1}{2 (8)}$

Step 3.2

Cancel the common factor.

$a_{3} = 2 \cdot \frac{1}{2 \cdot 8}$

Step 3.3

Rewrite the expression.

$a_{3} = \frac{1}{8}$

$a_{3} = \frac{1}{8}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$