Identify the Sequence 14 , 5 , -4 , -13

$14$ , $5$ , $- 4$ , $- 13$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 9$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 9$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 14$ and $d = - 9$ .

$a_{n} = 14 - 9 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 14 - 9 n - 9 \cdot - 1$

Multiply $- 9$ by $- 1$ .

$a_{n} = 14 - 9 n + 9$

Step 5

Add $14$ and $9$ .

$a_{n} = - 9 n + 23$

Identify the Sequence 14 , 5 , -4 , -13

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