Find the Next Term 10 , 2 , -6

$10$ , $2$ , $- 6$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 8$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 8$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 10$ and $d = - 8$ .

$a_{n} = 10 - 8 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 10 - 8 n - 8 \cdot - 1$

Multiply $- 8$ by $- 1$ .

$a_{n} = 10 - 8 n + 8$

Step 5

Add $10$ and $8$ .

$a_{n} = - 8 n + 18$

Step 6

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

$a_{4} = - 8 \cdot 4 + 18$

Step 7

Multiply $- 8$ by $4$ .

$a_{4} = - 32 + 18$

Step 8

Add $- 32$ and $18$ .

$a_{4} = - 14$

Find the Next Term 10 , 2 , -6

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