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

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

Step 1

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

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

Step 2

Add $3$ and $1$ .

$a_{3} = 3 \cdot (4)!$

Step 3

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

$a_{3} = 3 \cdot (4 \cdot 3 \cdot 2 \cdot 1)$

Step 4

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

Multiply $4$ by $3$ .

$a_{3} = 3 \cdot (12 \cdot 2 \cdot 1)$

Multiply $12$ by $2$ .

$a_{3} = 3 \cdot (24 \cdot 1)$

Multiply $24$ by $1$ .

$a_{3} = 3 \cdot 24$

Step 5

Multiply $3$ by $24$ .

$a_{3} = 72$