Identify the Sequence 3 , 9 , 15 , 21 , 27

$3$ , $9$ , $15$ , $21$ , $27$

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

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

Step 4

Simplify each term.

Apply the distributive property.

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

Multiply $6$ by $- 1$ .

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

Step 5

Subtract $6$ from $3$ .

$a_{n} = 6 n - 3$

Identify the Sequence 3 , 9 , 15 , 21 , 27

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