Precalculus Examples

$1$ , $\frac{1}{6}$ , $\frac{1}{36}$ , $\frac{1}{216}$

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 $\frac{1}{6}$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = \frac{1}{6}$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 1$ and $r = \frac{1}{6}$ .

$a_{n} = 1 {(\frac{1}{6})}^{n - 1}$

Step 4

Multiply ${(\frac{1}{6})}^{n - 1}$ by $1$ .

$a_{n} = {(\frac{1}{6})}^{n - 1}$

Step 5

Apply the product rule to $\frac{1}{6}$ .

$a_{n} = \frac{1^{n - 1}}{6^{n - 1}}$

Step 6

One to any power is one.

$a_{n} = \frac{1}{6^{n - 1}}$