Identify the Progression -4 , 12 , -36 , 108

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

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

Geometric Sequence: $r = - 3$

Step 2

This is the form of a geometric sequence.

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

Step 3

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

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

Identify the Progression -4 , 12 , -36 , 108

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