Answer
$a_{n}=\displaystyle \frac{n+2}{n+3}$
Work Step by Step
For $a_{1}$,
the numerator=1+2, the denominator = 1+3
For $a_{2}$,
the numerator=2+2, the denominator = 2+3
For $a_{3}$,
the numerator=3+2, the denominator = 3+3
For $a_{4}$,
the numerator=4+2, the denominator = 4+3
The subscripted index of the term is
increased by 2 to obtain the numerator, and
increased by 3 to obtain the denominator of the term.,
The pattern leads to the general term:
$a_{n}=\displaystyle \frac{n+2}{n+3}$
