Question

Sequences and series

Answer 1

Answer:

D

Step-by-step explanation:

$a_{n}=\frac{(n+3)!}{(n+3}=\frac{(n+3)(n+2)!}{n+3}=(n+2)!\\a_{1}=(1+2)!=3!=3*2*1=6\\a_{2}=(2+2)!=4!=4*3*2*1=24\\a_{3}=(3+2)=5!=5*4!=5*24=120\\a_{4}=(4=2)!=6!=6*5!=120*6=720\\a_{5}=(5+2)=7!=7*6!=720*7=5040$