Precalculus Examples

$8$ , $- 16$ , $32$ , $- 64$ , $128$

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

Geometric Sequence: $r = - 2$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 8$ and $r = - 2$ .

$a_{n} = 8 {(- 2)}^{n - 1}$

Step 4

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

$a_{7} = 8 {(- 2)}^{(7) - 1}$

Step 5

Subtract $1$ from $7$ .

$a_{7} = 8 {(- 2)}^{6}$

Step 6

Raise $- 2$ to the power of $6$ .

$a_{7} = 8 \cdot 64$

Step 7

Multiply $8$ by $64$ .

$a_{7} = 512$