Identify the Sequence -2 , -14 , -26 , -38

$- 2$ , $- 14$ , $- 26$ , $- 38$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 12$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 12$

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 $d = - 12$ .

$a_{n} = - 2 - 12 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = - 2 - 12 n - 12 \cdot - 1$

Multiply $- 12$ by $- 1$ .

$a_{n} = - 2 - 12 n + 12$

Step 5

Add $- 2$ and $12$ .

$a_{n} = - 12 n + 10$

Identify the Sequence -2 , -14 , -26 , -38

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