Precalculus Examples

$12$ , $30$ , $75$ , $187.5$

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 $\frac{5}{2}$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = \frac{5}{2}$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 12$ and $r = \frac{5}{2}$ .

$a_{n} = 12 {(\frac{5}{2})}^{n - 1}$

Step 4

Apply the product rule to $\frac{5}{2}$ .

$a_{n} = 12 \frac{5^{n - 1}}{2^{n - 1}}$

Step 5

Combine $12$ and $\frac{5^{n - 1}}{2^{n - 1}}$ .

$a_{n} = \frac{12 \cdot 5^{n - 1}}{2^{n - 1}}$