Identify the Sequence -3 , 2 , 7 , 12 , 17 , 22

$- 3$ , $2$ , $7$ , $12$ , $17$ , $22$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $5$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 5$

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 $d = 5$ .

$a_{n} = - 3 + 5 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = - 3 + 5 n + 5 \cdot - 1$

Multiply $5$ by $- 1$ .

$a_{n} = - 3 + 5 n - 5$

Step 5

Subtract $5$ from $- 3$ .

$a_{n} = 5 n - 8$

Identify the Sequence -3 , 2 , 7 , 12 , 17 , 22

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