Algebra Examples

$- \frac{2}{3}$ , $- 4$ , $- 24$ , $- 144$

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 $a_{1} = - \frac{2}{3}$ and $r = 6$ .

$a_{n} = - \frac{2}{3} \cdot 6^{n - 1}$

Step 4

Combine $6^{n - 1}$ and $\frac{2}{3}$ .

$a_{n} = - \frac{6^{n - 1} \cdot 2}{3}$

Step 5

Move $2$ to the left of $6^{n - 1}$ .

$a_{n} = - \frac{2 \cdot 6^{n - 1}}{3}$