Precalculus Examples

$6$ , $14$ , $22$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $8$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 8$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 6$ and $d = 8$ .

$a_{n} = 6 + 8 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$a_{n} = 6 + 8 n + 8 \cdot - 1$

Step 4.2

Multiply $8$ by $- 1$ .

$a_{n} = 6 + 8 n - 8$

Step 5

Subtract $8$ from $6$ .

$a_{n} = 8 n - 2$

Step 6

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

$a_{5} = 8 (5) - 2$

Step 7

Multiply $8$ by $5$ .

$a_{5} = 40 - 2$

Step 8

Subtract $2$ from $40$ .

$a_{5} = 38$

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