Algebra Examples

$- 1$ , $6$ , $- 36$ , $216$ ; dots

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

Geometric Sequence: $r = - 6$

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 $r = - 6$ .

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