Identify the Sequence 5 , -2 , -9 , -16

$5$ , $- 2$ , $- 9$ , $- 16$

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 $a_{1} = 5$ and $d = - 7$ .

$a_{n} = 5 - 7 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 5 - 7 n - 7 \cdot - 1$

Multiply $- 7$ by $- 1$ .

$a_{n} = 5 - 7 n + 7$

Step 5

Add $5$ and $7$ .

$a_{n} = - 7 n + 12$

Identify the Sequence 5 , -2 , -9 , -16

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