Precalculus Examples

$- \frac{3}{2}$ , $1$ , $\frac{7}{2}$ , $6$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $\frac{5}{2}$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = \frac{5}{2}$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = - \frac{3}{2}$ and $d = \frac{5}{2}$ .

$a_{n} = - \frac{3}{2} + \frac{5}{2} (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$a_{n} = - \frac{3}{2} + \frac{5}{2} n + \frac{5}{2} \cdot - 1$

Step 4.2

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

$a_{n} = - \frac{3}{2} + \frac{5 n}{2} + \frac{5}{2} \cdot - 1$

Step 4.3

Multiply $\frac{5}{2} \cdot - 1$ .

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Step 4.3.1

Combine $\frac{5}{2}$ and $- 1$ .

$a_{n} = - \frac{3}{2} + \frac{5 n}{2} + \frac{5 \cdot - 1}{2}$

Step 4.3.2

Multiply $5$ by $- 1$ .

$a_{n} = - \frac{3}{2} + \frac{5 n}{2} + \frac{- 5}{2}$

Step 4.4

Move the negative in front of the fraction.

$a_{n} = - \frac{3}{2} + \frac{5 n}{2} - \frac{5}{2}$

Step 5

Combine the numerators over the common denominator.

$a_{n} = \frac{- 3 + 5 n - 5}{2}$

Step 6

Subtract $5$ from $- 3$ .

$a_{n} = \frac{5 n - 8}{2}$