Identify the Sequence 7 , 1 , -5 , -11 , -17

$7$ , $1$ , $- 5$ , $- 11$ , $- 17$

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 $a_{1} = 7$ and $d = - 6$ .

$a_{n} = 7 - 6 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 7 - 6 n - 6 \cdot - 1$

Multiply $- 6$ by $- 1$ .

$a_{n} = 7 - 6 n + 6$

Step 5

Add $7$ and $6$ .

$a_{n} = - 6 n + 13$

Identify the Sequence 7 , 1 , -5 , -11 , -17

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