Precalculus Examples

$5$ , $\frac{11}{2}$ , $6$ , $\frac{13}{2}$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $\frac{1}{2}$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = \frac{1}{2}$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 5$ and $d = \frac{1}{2}$ .

$a_{n} = 5 + \frac{1}{2} (n - 1)$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Apply the distributive property.

$a_{n} = 5 + \frac{1}{2} n + \frac{1}{2} \cdot - 1$

Step 4.2

Combine $\frac{1}{2}$ and $n$ .

$a_{n} = 5 + \frac{n}{2} + \frac{1}{2} \cdot - 1$

Step 4.3

Combine $\frac{1}{2}$ and $- 1$ .

$a_{n} = 5 + \frac{n}{2} + \frac{- 1}{2}$

Step 4.4

Move the negative in front of the fraction.

$a_{n} = 5 + \frac{n}{2} - \frac{1}{2}$

Step 5

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$a_{n} = \frac{n}{2} + 5 \cdot \frac{2}{2} - \frac{1}{2}$

Step 6

Combine $5$ and $\frac{2}{2}$ .

$a_{n} = \frac{n}{2} + \frac{5 \cdot 2}{2} - \frac{1}{2}$

Step 7

Combine the numerators over the common denominator.

$a_{n} = \frac{n}{2} + \frac{5 \cdot 2 - 1}{2}$

Step 8

Simplify the numerator.

Tap for more steps...

Step 8.1

Multiply $5$ by $2$ .

$a_{n} = \frac{n}{2} + \frac{10 - 1}{2}$

Step 8.2

Subtract $1$ from $10$ .

$a_{n} = \frac{n}{2} + \frac{9}{2}$