Identify the Sequence 19 , 0 , -19 , -38

$19$ , $0$ , $- 19$ , $- 38$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 19$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 19$

Step 2

This is the formula of an arithmetic sequence.

$a_{n} = a_{1} + d (n - 1)$

Step 3

Substitute in the values of $a_{1} = 19$ and $d = - 19$ .

$a_{n} = 19 - 19 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 19 - 19 n - 19 \cdot - 1$

Multiply $- 19$ by $- 1$ .

$a_{n} = 19 - 19 n + 19$

Step 5

Add $19$ and $19$ .

$a_{n} = - 19 n + 38$

Identify the Sequence 19 , 0 , -19 , -38

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