Algebra Examples

8

$8$ ,

4

$4$ ,

2

$2$ ,

1

$1$

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

\frac{1}{2}

$\frac{1}{2}$ gives the next term. In other words,

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

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

Geometric Sequence:

r = \frac{1}{2}

$r = \frac{1}{2}$

Step 2

This is the form of a geometric sequence.

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

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

Step 3

Substitute in the values of

a_{1} = 8

$a_{1} = 8$ and

r = \frac{1}{2}

$r = \frac{1}{2}$ .

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

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

Step 4

Apply the product rule to

\frac{1}{2}

$\frac{1}{2}$ .

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

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

Step 5

One to any power is one.

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

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

Step 6

Combine

8

$8$ and

\frac{1}{2^{n - 1}}

$\frac{1}{2^{n - 1}}$ .

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

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

Step 7

Substitute in the value of

n

$n$ to find the

n

$n$ th term.

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

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

Step 8

Simplify the denominator.

Tap for more steps...

Step 8.1

Subtract

1

$1$ from

5

$5$ .

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

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

Step 8.2

Raise

2

$2$ to the power of

4

$4$ .

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

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

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

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

Step 9

Cancel the common factor of

8

$8$ and

16

$16$ .

Tap for more steps...

Step 9.1

Factor

8

$8$ out of

8

$8$ .

a_{5} = \frac{8 (1)}{16}

$a_{5} = \frac{8 (1)}{16}$

Step 9.2

Cancel the common factors.

Tap for more steps...

Step 9.2.1

Factor

8

$8$ out of

16

$16$ .

a_{5} = \frac{8 \cdot 1}{8 \cdot 2}

$a_{5} = \frac{8 \cdot 1}{8 \cdot 2}$

Step 9.2.2

Cancel the common factor.

a_{5} = \frac{8 \cdot 1}{8 \cdot 2}

$a_{5} = \frac{8 \cdot 1}{8 \cdot 2}$

Step 9.2.3

Rewrite the expression.

a_{5} = \frac{1}{2}

$a_{5} = \frac{1}{2}$

a_{5} = \frac{1}{2}

$a_{5} = \frac{1}{2}$

a_{5} = \frac{1}{2}

$a_{5} = \frac{1}{2}$