Find the Third Term a_n=((n+1)!)/(n+1)

$a_{n} = \frac{(n + 1)!}{n + 1}$

Step 1

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

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

Step 2

Simplify the numerator.

Add $3$ and $1$ .

$a_{3} = \frac{(4)!}{3 + 1}$

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

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

Multiply $4 \cdot 3 \cdot 2 \cdot 1$ .

Multiply $4$ by $3$ .

$a_{3} = \frac{12 \cdot 2 \cdot 1}{3 + 1}$

Multiply $12$ by $2$ .

$a_{3} = \frac{24 \cdot 1}{3 + 1}$

Multiply $24$ by $1$ .

$a_{3} = \frac{24}{3 + 1}$

Step 3

Simplify the expression.

Add $3$ and $1$ .

$a_{3} = \frac{24}{4}$

Divide $24$ by $4$ .

$a_{3} = 6$