Algebra Examples

$\frac{5}{6}$ , $\frac{2}{3}$ , $\frac{1}{2}$ , $\frac{1}{3}$

Step 1

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: $d = - \frac{1}{6}$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = \frac{5}{6}$ and $d = - \frac{1}{6}$ .

$a_{n} = \frac{5}{6} - \frac{1}{6} (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$a_{n} = \frac{5}{6} - \frac{1}{6} n - \frac{1}{6} \cdot - 1$

Step 4.2

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

$a_{n} = \frac{5}{6} - \frac{n}{6} - \frac{1}{6} \cdot - 1$

Step 4.3

Multiply $- \frac{1}{6} \cdot - 1$ .

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Step 4.3.1

Multiply $- 1$ by $- 1$ .

$a_{n} = \frac{5}{6} - \frac{n}{6} + 1 (\frac{1}{6})$

Step 4.3.2

Multiply $\frac{1}{6}$ by $1$ .

$a_{n} = \frac{5}{6} - \frac{n}{6} + \frac{1}{6}$

Step 5

Combine the numerators over the common denominator.

$a_{n} = \frac{5 - n + 1}{6}$

Step 6

Add $5$ and $1$ .

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