Algebra Examples

\frac{1}{4}

$\frac{1}{4}$ ,

\frac{5}{16}

$\frac{5}{16}$ ,

\frac{3}{8}

$\frac{3}{8}$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding

\frac{1}{16}

$\frac{1}{16}$ to the previous term in the sequence gives the next term. In other words,

a_{n} = a_{1} + d (n - 1)

$a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence:

d = \frac{1}{16}

$d = \frac{1}{16}$

Step 2

This is the formula of an arithmetic sequence.

a_{n} = a_{1} + d (n - 1)

$a_{n} = a_{1} + d (n - 1)$

Step 3

Substitute in the values of

a_{1} = \frac{1}{4}

$a_{1} = \frac{1}{4}$ and

d = \frac{1}{16}

$d = \frac{1}{16}$ .

a_{n} = \frac{1}{4} + \frac{1}{16} (n - 1)

$a_{n} = \frac{1}{4} + \frac{1}{16} (n - 1)$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Apply the distributive property.

a_{n} = \frac{1}{4} + \frac{1}{16} n + \frac{1}{16} \cdot - 1

$a_{n} = \frac{1}{4} + \frac{1}{16} n + \frac{1}{16} \cdot - 1$

Step 4.2

Combine

\frac{1}{16}

$\frac{1}{16}$ and

n

$n$ .

a_{n} = \frac{1}{4} + \frac{n}{16} + \frac{1}{16} \cdot - 1

$a_{n} = \frac{1}{4} + \frac{n}{16} + \frac{1}{16} \cdot - 1$

Step 4.3

Combine

\frac{1}{16}

$\frac{1}{16}$ and

- 1

$- 1$ .

a_{n} = \frac{1}{4} + \frac{n}{16} + \frac{- 1}{16}

$a_{n} = \frac{1}{4} + \frac{n}{16} + \frac{- 1}{16}$

Step 4.4

Move the negative in front of the fraction.

a_{n} = \frac{1}{4} + \frac{n}{16} - \frac{1}{16}

$a_{n} = \frac{1}{4} + \frac{n}{16} - \frac{1}{16}$

a_{n} = \frac{1}{4} + \frac{n}{16} - \frac{1}{16}

$a_{n} = \frac{1}{4} + \frac{n}{16} - \frac{1}{16}$

Step 5

To write

\frac{1}{4}

$\frac{1}{4}$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

a_{n} = \frac{n}{16} + \frac{1}{4} \cdot \frac{4}{4} - \frac{1}{16}

$a_{n} = \frac{n}{16} + \frac{1}{4} \cdot \frac{4}{4} - \frac{1}{16}$

Step 6

Write each expression with a common denominator of

16

$16$ , by multiplying each by an appropriate factor of

1

$1$ .

Tap for more steps...

Step 6.1

Multiply

\frac{1}{4}

$\frac{1}{4}$ by

\frac{4}{4}

$\frac{4}{4}$ .

a_{n} = \frac{n}{16} + \frac{4}{4 \cdot 4} - \frac{1}{16}

$a_{n} = \frac{n}{16} + \frac{4}{4 \cdot 4} - \frac{1}{16}$

Step 6.2

Multiply

4

$4$ by

4

$4$ .

a_{n} = \frac{n}{16} + \frac{4}{16} - \frac{1}{16}

$a_{n} = \frac{n}{16} + \frac{4}{16} - \frac{1}{16}$

a_{n} = \frac{n}{16} + \frac{4}{16} - \frac{1}{16}

$a_{n} = \frac{n}{16} + \frac{4}{16} - \frac{1}{16}$

Step 7

Combine the numerators over the common denominator.

a_{n} = \frac{n}{16} + \frac{4 - 1}{16}

$a_{n} = \frac{n}{16} + \frac{4 - 1}{16}$

Step 8

Subtract

1

$1$ from

4

$4$ .

a_{n} = \frac{n}{16} + \frac{3}{16}

$a_{n} = \frac{n}{16} + \frac{3}{16}$