Find the 5th Term 21 , 15 , 9 , 3

$21$ , $15$ , $9$ , $3$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 6$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 6$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 21$ and $d = - 6$ .

$a_{n} = 21 - 6 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 21 - 6 n - 6 \cdot - 1$

Multiply $- 6$ by $- 1$ .

$a_{n} = 21 - 6 n + 6$

Step 5

Add $21$ and $6$ .

$a_{n} = - 6 n + 27$

Step 6

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

$a_{5} = - 6 \cdot 5 + 27$

Step 7

Multiply $- 6$ by $5$ .

$a_{5} = - 30 + 27$

Step 8

Add $- 30$ and $27$ .

$a_{5} = - 3$

Find the 5th Term 21 , 15 , 9 , 3

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