Identify the Sequence 9 , 18 , 27

$9$ , $18$ , $27$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $9$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 9$

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 $d = 9$ .

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

Step 4

Simplify each term.

Apply the distributive property.

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

Multiply $9$ by $- 1$ .

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

Step 5

Combine the opposite terms in $9 + 9 n - 9$ .

Subtract $9$ from $9$ .

$a_{n} = 9 n + 0$

Add $9 n$ and $0$ .

$a_{n} = 9 n$

Identify the Sequence 9 , 18 , 27

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