Find the Next Term 6 , 2 , -2 , -6

$6$ , $2$ , $- 2$ , $- 6$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 4$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 4$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 6$ and $d = - 4$ .

$a_{n} = 6 - 4 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 6 - 4 n - 4 \cdot - 1$

Multiply $- 4$ by $- 1$ .

$a_{n} = 6 - 4 n + 4$

Step 5

Add $6$ and $4$ .

$a_{n} = - 4 n + 10$

Step 6

Substitute in the value of $n$ to find the $n$ th term.

$a_{5} = - 4 \cdot 5 + 10$

Step 7

Multiply $- 4$ by $5$ .

$a_{5} = - 20 + 10$

Step 8

Add $- 20$ and $10$ .

$a_{5} = - 10$

Find the Next Term 6 , 2 , -2 , -6

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