Question

Determine the first four terms of the sequence in which the nth term is

Answer 1

Answer:

The correct answer option is: $\frac{1}{3} ,\frac{1}{4} ,\frac{1}{5} ,\frac{1}{6}$.

Step-by-step explanation:

We know that the $nth$ term $a_n$ for an arithmetic sequence is given by:

$a_n=\frac{(n+1)!}{(n+2)!}$

where $n$ 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 $n$ from 1 to 4 in the given formula to get:

1st term:

$a_1=\frac{(1+1)!}{(1+2)!}=\frac{1}{3}$

2nd term:

$a_2=\frac{(2+1)!}{(2+2)!}=\frac{1}{4}$

3rd term:

$a_3=\frac{(3+1)!}{(3+2)!}=\frac{1}{5}$

4th term:

$a_4=\frac{(4+1)!}{(4+2)!}=\frac{1}{6}$