Identify the Sequence -3 , -23 , -43 , -63

$- 3$ , $- 23$ , $- 43$ , $- 63$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 20$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 20$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = - 3$ and $d = - 20$ .

$a_{n} = - 3 - 20 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = - 3 - 20 n - 20 \cdot - 1$

Multiply $- 20$ by $- 1$ .

$a_{n} = - 3 - 20 n + 20$

Step 5

Add $- 3$ and $20$ .

$a_{n} = - 20 n + 17$

Identify the Sequence -3 , -23 , -43 , -63

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