Precalculus Examples

$20$ , $18.5$ , $17$ , $15.5$ , $14$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 1.5$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 1.5$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 20$ and $d = - 1.5$ .

$a_{n} = 20 - 1.5 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$a_{n} = 20 - 1.5 n - 1.5 \cdot - 1$

Step 4.2

Multiply $- 1.5$ by $- 1$ .

$a_{n} = 20 - 1.5 n + 1.5$

Step 5

Add $20$ and $1.5$ .

$a_{n} = - 1.5 n + 21.5$