Algebra Examples

$\frac{3}{8}$ , $- 3$ , $24$ , $- 192$

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 $a_{1} = \frac{3}{8}$ and $r = - 8$ .

$a_{n} = \frac{3}{8} {(- 8)}^{n - 1}$

Step 4

Combine $\frac{3}{8}$ and ${(- 8)}^{n - 1}$ .

$a_{n} = \frac{3 {(- 8)}^{n - 1}}{8}$

Step 5

Cancel the common factor of ${(- 8)}^{n - 1}$ and $8$ .

Tap for more steps...

Step 5.1

Rewrite $8$ as $- 1 (- 8)$ .

$a_{n} = \frac{3 {(- 8)}^{n - 1}}{- 1 (- 8)}$

Step 5.2

Factor $- 8$ out of $3 {(- 8)}^{n - 1}$ .

$a_{n} = \frac{- 8 (3 {(- 8)}^{n - 2})}{- 1 (- 8)}$

Step 5.3

Move the negative one from the denominator of $\frac{3 {(- 8)}^{n - 2}}{- 1}$ .

$a_{n} = - 1 \cdot (3 {(- 8)}^{n - 2})$

Step 6

Rewrite $- 1 \cdot (3 {(- 8)}^{n - 2})$ as $- (3 {(- 8)}^{n - 2})$ .

$a_{n} = - (3 {(- 8)}^{n - 2})$

Step 7

Multiply $3$ by $- 1$ .

$a_{n} = - 3 {(- 8)}^{n - 2}$