Algebra Examples

$3$ , $- 12$ , $48$ , $- 192$

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 $- 4$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = - 4$

This is the form of a geometric sequence.

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

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

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