Identify the Sequence 4 , 1 , -2 , -5

$4$ , $1$ , $- 2$ , $- 5$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 3$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 3$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 4$ and $d = - 3$ .

$a_{n} = 4 - 3 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 4 - 3 n - 3 \cdot - 1$

Multiply $- 3$ by $- 1$ .

$a_{n} = 4 - 3 n + 3$

Step 5

Add $4$ and $3$ .

$a_{n} = - 3 n + 7$

Identify the Sequence 4 , 1 , -2 , -5

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