Algebra Examples

$9$ , $15$ , $21$ , $27$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $6$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 6$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 9$ and $d = 6$ .

$a_{n} = 9 + 6 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$a_{n} = 9 + 6 n + 6 \cdot - 1$

Step 4.2

Multiply $6$ by $- 1$ .

$a_{n} = 9 + 6 n - 6$

Step 5

Subtract $6$ from $9$ .

$a_{n} = 6 n + 3$

Step 6

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

$a_{5} = 6 (5) + 3$

Step 7

Multiply $6$ by $5$ .

$a_{5} = 30 + 3$

Step 8

Add $30$ and $3$ .

$a_{5} = 33$