Algebra Examples

$\frac{1}{128}$ , $- \frac{1}{16}$ , $\frac{1}{2}$ , $- 4$ , $32$

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 $- 8$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = - 8$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = \frac{1}{128}$ and $r = - 8$ .

$a_{n} = \frac{1}{128} {(- 8)}^{n - 1}$

Step 4

Combine $\frac{1}{128}$ and ${(- 8)}^{n - 1}$ .

$a_{n} = \frac{{(- 8)}^{n - 1}}{128}$

Step 5

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

$a_{6} = \frac{{(- 8)}^{(6) - 1}}{128}$

Step 6

Simplify the numerator.

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Step 6.1

Subtract $1$ from $6$ .

$a_{6} = \frac{{(- 8)}^{5}}{128}$

Step 6.2

Raise $- 8$ to the power of $5$ .

$a_{6} = \frac{- 32768}{128}$

Step 7

Divide $- 32768$ by $128$ .

$a_{6} = - 256$