Precalculus Examples

$11$ , $- 44$ , $176$

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

Geometric Sequence: $r = - 4$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 11$ and $r = - 4$ .

$a_{n} = 11 {(- 4)}^{n - 1}$

Step 4

Substitute in the value of $n$ to find the $n$ th term.

$a_{5} = 11 {(- 4)}^{(5) - 1}$

Step 5

Subtract $1$ from $5$ .

$a_{5} = 11 {(- 4)}^{4}$

Step 6

Raise $- 4$ to the power of $4$ .

$a_{5} = 11 \cdot 256$

Step 7

Multiply $11$ by $256$ .

$a_{5} = 2816$