Identify the Sequence 6 , 9 , 12 , 15

$6$ , $9$ , $12$ , $15$

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 $a_{1} = 6$ and $d = 3$ .

$a_{n} = 6 + 3 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 6 + 3 n + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$a_{n} = 6 + 3 n - 3$

Step 5

Subtract $3$ from $6$ .

$a_{n} = 3 n + 3$

Identify the Sequence 6 , 9 , 12 , 15

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