Identify the Sequence 5 , -1 , -7 , -13 , -19

$5$ , $- 1$ , $- 7$ , $- 13$ , $- 19$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 6$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 6$

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 $d = - 6$ .

$a_{n} = 5 - 6 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 5 - 6 n - 6 \cdot - 1$

Multiply $- 6$ by $- 1$ .

$a_{n} = 5 - 6 n + 6$

Step 5

Add $5$ and $6$ .

$a_{n} = - 6 n + 11$

Identify the Sequence 5 , -1 , -7 , -13 , -19

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