Identify the Sequence -2 , 5 , 12 , 19

$- 2$ , $5$ , $12$ , $19$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $7$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 7$

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 $d = 7$ .

$a_{n} = - 2 + 7 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = - 2 + 7 n + 7 \cdot - 1$

Multiply $7$ by $- 1$ .

$a_{n} = - 2 + 7 n - 7$

Step 5

Subtract $7$ from $- 2$ .

$a_{n} = 7 n - 9$

Identify the Sequence -2 , 5 , 12 , 19

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