Algebra Examples

$12$ , $5$ , $- 2$ , $- 9$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 7$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 7$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 12$ and $d = - 7$ .

$a_{n} = 12 - 7 (n - 1)$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$a_{n} = 12 - 7 n - 7 \cdot - 1$

Step 4.2

Multiply $- 7$ by $- 1$ .

$a_{n} = 12 - 7 n + 7$

Step 5

Add $12$ and $7$ .

$a_{n} = - 7 n + 19$