Algebra Examples

$- 512$ , $- 128$ , $- 32$ , $- 8$

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 $a_{1} = - 512$ and $r = \frac{1}{4}$ .

$a_{n} = - 512 {(\frac{1}{4})}^{n - 1}$

Step 4

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

$a_{n} = - 512 \frac{1^{n - 1}}{4^{n - 1}}$

Step 5

One to any power is one.

$a_{n} = - 512 \frac{1}{4^{n - 1}}$

Step 6

Combine $- 512$ and $\frac{1}{4^{n - 1}}$ .

$a_{n} = \frac{- 512}{4^{n - 1}}$

Step 7

Move the negative in front of the fraction.

$a_{n} = - \frac{512}{4^{n - 1}}$

Step 8

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

$a_{5} = - \frac{512}{4^{(5) - 1}}$

Step 9

Simplify the denominator.

Tap for more steps...

Step 9.1

Subtract $1$ from $5$ .

$a_{5} = - \frac{512}{4^{4}}$

Step 9.2

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

$a_{5} = - \frac{512}{256}$

Step 10

Simplify the expression.

Tap for more steps...

Step 10.1

Divide $512$ by $256$ .

$a_{5} = - 1 \cdot 2$

Step 10.2

Multiply $- 1$ by $2$ .

$a_{5} = - 2$