Find the Next Term -6 , -9 , -12 , -15 , -18

$- 6$ , $- 9$ , $- 12$ , $- 15$ , $- 18$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 3$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 3$

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 $d = - 3$ .

$a_{n} = - 6 - 3 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = - 6 - 3 n - 3 \cdot - 1$

Multiply $- 3$ by $- 1$ .

$a_{n} = - 6 - 3 n + 3$

Step 5

Add $- 6$ and $3$ .

$a_{n} = - 3 n - 3$

Step 6

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

$a_{6} = - 3 \cdot 6 - 3$

Step 7

Multiply $- 3$ by $6$ .

$a_{6} = - 18 - 3$

Step 8

Subtract $3$ from $- 18$ .

$a_{6} = - 21$

Find the Next Term -6 , -9 , -12 , -15 , -18

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