Algebra Examples

$3$ , $2$ , $\frac{4}{3}$

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 $\frac{2}{3}$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = \frac{2}{3}$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 3$ and $r = \frac{2}{3}$ .

$a_{n} = 3 {(\frac{2}{3})}^{n - 1}$

Step 4

Apply the product rule to $\frac{2}{3}$ .

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

Step 5

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

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