Algebra 2 (1st Edition)

n-th term:$\quad a_{n}=\displaystyle \frac{2n}{n+2}$ The next term is $\displaystyle \quad a_{5}=\frac{10}{7}$
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 $a_{5}=\displaystyle \frac{2\cdot 5}{5+2}=\frac{10}{7}$