Answer
$a_n=\frac{1}{n+1}$
Work Step by Step
We are given the sequence:
$\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5}, . . .$
In order to find the general term we must determine the pattern:
$a_1=\frac{1}{2}=\frac{1}{1+1}$
$a_2=\frac{1}{3}=\frac{1}{2+1}$
$a_3=\frac{1}{4}=\frac{1}{3+1}$
$a_4=\frac{1}{5}=\frac{1}{4+1}$
We notice that the general term is a fraction with numerator $1$ and denominator equal to the position of the term in the sequence plus one.
The general term $a_n$ will look like
$a_n=\dfrac{1}{n+1},$ where $n=1,2,3, . . .$
