Answer:
Third option 2,6,24,120,720
Step-by-step explanation:
Step 1
The first step is to simplify the expression for the nth term of this sequence using the definition of the factorial symbol. The simplification of this expression is done below,
[tex]a_n=\frac{(n+2)!}{(n+2)}=\frac{(n+2)\times(n+1)!}{(n+2)} =(n+1)![/tex]
Step 2
The second step is to use the substitute different values of n into the expression of the nth term to work out which sequence corresponds to the correct answer.
[tex]a_1=(1+1)!=2!=2\\a_2=(2+1)!=3!=6\\a_3=(3+1)!=4!=24\\a_4=(4+1)!=5!=120\\a_5=(5+1)!=6!=720[/tex]
The terms of the sequence are {2,6,24,120,720}. The correct answer is the third option.
