Algebra Examples

$\frac{2}{3}$ , $\frac{1}{6}$ , $\frac{1}{24}$ , $\frac{1}{96}$

Step 1

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by $\frac{1}{4}$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = \frac{1}{4}$

Step 2

This is the form of a geometric sequence.

$a_{n} = a_{1} r^{n - 1}$

Step 3

Substitute in the values of $a_{1} = \frac{2}{3}$ and $r = \frac{1}{4}$ .

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

Step 4

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

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

Step 5

Combine.

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

Step 6

One to any power is one.

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

Step 7

Multiply $2$ by $1$ .

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