Find the 3rd Term (n/(n+6))

$(\frac{n}{n + 6})$

Step 1

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

$a_{3} = \frac{3}{(3) + 6}$

Step 2

Remove parentheses.

$a_{3} = \frac{3}{(3) + 6}$

Step 3

Cancel the common factor of $3$ and $(3) + 6$ .

Factor $3$ out of $3$ .

$a_{3} = \frac{3 \cdot 1}{3 + 6}$

Cancel the common factors.

Factor $3$ out of $3$ .

$a_{3} = \frac{3 \cdot 1}{3 (1) + 6}$

Factor $3$ out of $6$ .

$a_{3} = \frac{3 \cdot 1}{3 \cdot 1 + 3 \cdot 2}$

Factor $3$ out of $3 \cdot 1 + 3 \cdot 2$ .

$a_{3} = \frac{3 \cdot 1}{3 \cdot (1 + 2)}$

Cancel the common factor.

$a_{3} = \frac{3 \cdot 1}{3 \cdot (1 + 2)}$

Rewrite the expression.

$a_{3} = \frac{1}{1 + 2}$

Step 4

Add $1$ and $2$ .

$a_{3} = \frac{1}{3}$