Algebra Examples

$3$ , $6$ , $9$ , $12$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $3$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 3$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 3$ and $d = 3$ .

$a_{n} = 3 + 3 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

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

Step 4.2

Multiply $3$ by $- 1$ .

$a_{n} = 3 + 3 n - 3$

Step 5

Combine the opposite terms in $3 + 3 n - 3$ .

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Step 5.1

Subtract $3$ from $3$ .

$a_{n} = 3 n + 0$

Step 5.2

Add $3 n$ and $0$ .

$a_{n} = 3 n$