Algebra Examples

$\frac{1}{4}$ , $\frac{5}{16}$ , $\frac{3}{8}$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $\frac{1}{16}$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = \frac{1}{16}$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = \frac{1}{4}$ and $d = \frac{1}{16}$ .

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

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Apply the distributive property.

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

Step 4.2

Combine $\frac{1}{16}$ and $n$ .

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

Step 4.3

Combine $\frac{1}{16}$ and $- 1$ .

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

Step 4.4

Move the negative in front of the fraction.

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

Step 5

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

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

Step 6

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 6.1

Multiply $\frac{1}{4}$ by $\frac{4}{4}$ .

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

Step 6.2

Multiply $4$ by $4$ .

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

Step 7

Combine the numerators over the common denominator.

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

Step 8

Subtract $1$ from $4$ .

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