Find the 6th Term -10 , -6 , -2 , 2

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

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 $a_{1} = - 10$ and $d = 4$ .

$a_{n} = - 10 + 4 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = - 10 + 4 n + 4 \cdot - 1$

Multiply $4$ by $- 1$ .

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

Step 5

Subtract $4$ from $- 10$ .

$a_{n} = 4 n - 14$

Step 6

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

$a_{6} = 4 (6) - 14$

Step 7

Multiply $4$ by $6$ .

$a_{6} = 24 - 14$

Step 8

Subtract $14$ from $24$ .

$a_{6} = 10$

Find the 6th Term -10 , -6 , -2 , 2

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