Answer:
The correct answer option is: [tex]\frac{1}{3} ,\frac{1}{4} ,\frac{1}{5} ,\frac{1}{6}[/tex].
Step-by-step explanation:
We know that the [tex]nth[/tex] term [tex]a_n[/tex] for an arithmetic sequence is given by:
[tex]a_n=\frac{(n+1)!}{(n+2)!}[/tex]
where [tex]n[/tex] is the number of the position of the term.
We are supposed to find the first four terms of the sequence so we will substitute the values of [tex]n[/tex] from 1 to 4 in the given formula to get:
1st term:
[tex]a_1=\frac{(1+1)!}{(1+2)!}=\frac{1}{3}[/tex]
2nd term:
[tex]a_2=\frac{(2+1)!}{(2+2)!}=\frac{1}{4}[/tex]
3rd term:
[tex]a_3=\frac{(3+1)!}{(3+2)!}=\frac{1}{5}[/tex]
4th term:
[tex]a_4=\frac{(4+1)!}{(4+2)!}=\frac{1}{6}[/tex]
