Find the Next Term 1/6 , 1/3 , 1/2 , 2/3

$\frac{1}{6}$ , $\frac{1}{3}$ , $\frac{1}{2}$ , $\frac{2}{3}$

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $\frac{1}{6}$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = \frac{1}{6}$

This is the formula of an arithmetic sequence.

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

Substitute in the values of $a_{1} = \frac{1}{6}$ and $d = \frac{1}{6}$ .

$a_{n} = \frac{1}{6} + \frac{1}{6} (n - 1)$

Simplify each term.

Apply the distributive property.

$a_{n} = \frac{1}{6} + \frac{1}{6} n + \frac{1}{6} \cdot - 1$

Combine $\frac{1}{6}$ and $n$ .

$a_{n} = \frac{1}{6} + \frac{n}{6} + \frac{1}{6} \cdot - 1$

Combine $\frac{1}{6}$ and $- 1$ .

$a_{n} = \frac{1}{6} + \frac{n}{6} + \frac{- 1}{6}$

Move the negative in front of the fraction.

$a_{n} = \frac{1}{6} + \frac{n}{6} - \frac{1}{6}$

Combine the opposite terms in $\frac{1}{6} + \frac{n}{6} - \frac{1}{6}$ .

Combine the numerators over the common denominator.

$a_{n} = \frac{n}{6} + \frac{1 - 1}{6}$

Subtract $1$ from $1$ .

$a_{n} = \frac{n}{6} + \frac{0}{6}$

Divide $0$ by $6$ .

$a_{n} = \frac{n}{6} + 0$

Add $\frac{n}{6}$ and $0$ .

$a_{n} = \frac{n}{6}$

Substitute in the value of $n$ to find the $n$ th term.

$a_{5} = \frac{5}{6}$

Find the Next Term 1/6 , 1/3 , 1/2 , 2/3

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