Identify the Sequence 2 , 4 , 6

$2$ , $4$ , $6$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $2$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 2$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 2$ and $d = 2$ .

$a_{n} = 2 + 2 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 2 + 2 n + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$a_{n} = 2 + 2 n - 2$

Step 5

Combine the opposite terms in $2 + 2 n - 2$ .

Subtract $2$ from $2$ .

$a_{n} = 2 n + 0$

Add $2 n$ and $0$ .

$a_{n} = 2 n$

Identify the Sequence 2 , 4 , 6

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