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

$3$ , $- 2$ , $- 7$ , $- 12$

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

Add $3$ and $5$ .

$a_{n} = - 5 n + 8$

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

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