Identify the Sequence 1/8 , 1/4 , 3/8 , 1/2

$\frac{1}{8}$ , $\frac{1}{4}$ , $\frac{3}{8}$ , $\frac{1}{2}$

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $\frac{1}{8}$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = \frac{1}{8}$

This is the formula of an arithmetic sequence.

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

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

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

Simplify each term.

Apply the distributive property.

$a_{n} = \frac{1}{8} + \frac{1}{8} n + \frac{1}{8} \cdot - 1$

Combine $\frac{1}{8}$ and $n$ .

$a_{n} = \frac{1}{8} + \frac{n}{8} + \frac{1}{8} \cdot - 1$

Combine $\frac{1}{8}$ and $- 1$ .

$a_{n} = \frac{1}{8} + \frac{n}{8} + \frac{- 1}{8}$

Move the negative in front of the fraction.

$a_{n} = \frac{1}{8} + \frac{n}{8} - \frac{1}{8}$

Combine the opposite terms in $\frac{1}{8} + \frac{n}{8} - \frac{1}{8}$ .

Combine the numerators over the common denominator.

$a_{n} = \frac{n}{8} + \frac{1 - 1}{8}$

Subtract $1$ from $1$ .

$a_{n} = \frac{n}{8} + \frac{0}{8}$

Divide $0$ by $8$ .

$a_{n} = \frac{n}{8} + 0$

Add $\frac{n}{8}$ and $0$ .

$a_{n} = \frac{n}{8}$

Identify the Sequence 1/8 , 1/4 , 3/8 , 1/2

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