Identify the Sequence 5 , 3 , 1 , -1

$5$ , $3$ , $1$ , $- 1$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 2$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 2$

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 $d = - 2$ .

$a_{n} = 5 - 2 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 5 - 2 n - 2 \cdot - 1$

Multiply $- 2$ by $- 1$ .

$a_{n} = 5 - 2 n + 2$

Step 5

Add $5$ and $2$ .

$a_{n} = - 2 n + 7$

Identify the Sequence 5 , 3 , 1 , -1

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