Identify the Sequence -3 , -6 , -9 , -12

$- 3$ , $- 6$ , $- 9$ , $- 12$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 3$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 3$

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 $d = - 3$ .

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

Step 4

Simplify each term.

Apply the distributive property.

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

Multiply $- 3$ by $- 1$ .

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

Step 5

Combine the opposite terms in $- 3 - 3 n + 3$ .

Add $- 3$ and $3$ .

$a_{n} = - 3 n + 0$

Add $- 3 n$ and $0$ .

$a_{n} = - 3 n$

Identify the Sequence -3 , -6 , -9 , -12

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