Precalculus Examples

$12$ , $6$ , $3$ , $1.5$

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 $\frac{1}{2}$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = \frac{1}{2}$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 12$ and $r = \frac{1}{2}$ .

$a_{n} = 12 {(\frac{1}{2})}^{n - 1}$

Step 4

Apply the product rule to $\frac{1}{2}$ .

$a_{n} = 12 \frac{1^{n - 1}}{2^{n - 1}}$

Step 5

One to any power is one.

$a_{n} = 12 \frac{1}{2^{n - 1}}$

Step 6

Combine $12$ and $\frac{1}{2^{n - 1}}$ .

$a_{n} = \frac{12}{2^{n - 1}}$