Precalculus Examples

$3$ , $- 6$ , $12$ , $- 24$

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

Geometric Sequence: $r = - 2$

Step 2

This is the form of a geometric sequence.

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

Step 3

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

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

Step 4

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

$a_{6} = 3 {(- 2)}^{(6) - 1}$

Step 5

Subtract $1$ from $6$ .

$a_{6} = 3 {(- 2)}^{5}$

Step 6

Raise $- 2$ to the power of $5$ .

$a_{6} = 3 \cdot - 32$

Step 7

Multiply $3$ by $- 32$ .

$a_{6} = - 96$