Find the Third Term a_n=((n+4)!)/((n+5)!)

$a_{n} = \frac{(n + 4)!}{(n + 5)!}$

Step 1

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

$a_{3} = \frac{((3) + 4)!}{((3) + 5)!}$

Step 2

Simplify the factorials.

Add $3$ and $4$ .

$a_{3} = \frac{(7)!}{((3) + 5)!}$

Add $3$ and $5$ .

$a_{3} = \frac{(7)!}{(8)!}$

Step 3

Rewrite $(8)!$ as $8 \cdot 7!$ .

$a_{3} = \frac{(7)!}{8 \cdot 7!}$

Step 4

Cancel the common factor of $(7)!$ .

Cancel the common factor.

$a_{3} = \frac{(7)!}{8 \cdot 7!}$

Rewrite the expression.

$a_{3} = \frac{1}{8}$