Find the 5th Term -1/8 , -1/4 , -1/2 , -1

$- \frac{1}{8}$ , $- \frac{1}{4}$ , $- \frac{1}{2}$ , $- 1$

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 $a_{1} = - \frac{1}{8}$ and $r = 2$ .

$a_{n} = - \frac{1}{8} \cdot 2^{n - 1}$

Step 4

Combine $2^{n - 1}$ and $\frac{1}{8}$ .

$a_{n} = - \frac{2^{n - 1}}{8}$

Step 5

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

$a_{5} = - \frac{2^{(5) - 1}}{8}$

Step 6

Simplify the numerator.

Subtract $1$ from $5$ .

$a_{5} = - \frac{2^{4}}{8}$

Raise $2$ to the power of $4$ .

$a_{5} = - \frac{16}{8}$

Step 7

Simplify the expression.

Divide $16$ by $8$ .

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

Multiply $- 1$ by $2$ .

$a_{5} = - 2$

Find the 5th Term -1/8 , -1/4 , -1/2 , -1

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