Answer
n-th term:$\quad a_{n}=\displaystyle \frac{2n}{n+2}$
The next term is $\displaystyle \quad a_{5}=\frac{10}{7}$
Work Step by Step
The n-th numerator is a multiple of 2, starting with $2(1).$
The first denominator is $3 = 2+1$,
The 2nd denominator is $4 = 2+2,$
The 3rd denominator is $5 = 2+3,$
$...$
The nth denominator is $2+n$
So, the nth term is $a_{n}=\displaystyle \frac{2n}{n+2}$,
and the next term is $a_{5}=\displaystyle \frac{2\cdot 5}{5+2}=\frac{10}{7}$
