Find the Third Term a_n=((n+2)!)/(n+2)

$a_{n} = \frac{(n + 2)!}{n + 2}$

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

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

Simplify the numerator.

Add $3$ and $2$ .

$a_{3} = \frac{(5)!}{3 + 2}$

Expand $(5)!$ to $5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$a_{3} = \frac{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{3 + 2}$

Simplify.

Multiply $5$ by $4$ .

$a_{3} = \frac{20 \cdot 3 \cdot 2 \cdot 1}{3 + 2}$

Multiply $20$ by $3$ .

$a_{3} = \frac{60 \cdot 2 \cdot 1}{3 + 2}$

Multiply $60$ by $2$ .

$a_{3} = \frac{120 \cdot 1}{3 + 2}$

Multiply $120$ by $1$ .

$a_{3} = \frac{120}{3 + 2}$

Simplify the expression.

Add $3$ and $2$ .

$a_{3} = \frac{120}{5}$

Divide $120$ by $5$ .

$a_{3} = 24$