Precalculus Examples

$400$ , $100$ , $25$ , $6.25$

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 $\frac{1}{4}$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = \frac{1}{4}$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 400$ and $r = \frac{1}{4}$ .

$a_{n} = 400 {(\frac{1}{4})}^{n - 1}$

Step 4

Apply the product rule to $\frac{1}{4}$ .

$a_{n} = 400 \frac{1^{n - 1}}{4^{n - 1}}$

Step 5

One to any power is one.

$a_{n} = 400 \frac{1}{4^{n - 1}}$

Step 6

Combine $400$ and $\frac{1}{4^{n - 1}}$ .

$a_{n} = \frac{400}{4^{n - 1}}$