Algebra Examples

$4$ , $- 12$ , $36$ , $- 108$

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 $- 3$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = - 3$

This is the form of a geometric sequence.

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

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

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