It'a an arithmetic sequence:
[tex]a_1=-1\\\\a_2=-1+\dfrac{5}{3}=-\dfrac{3}{3}+\dfrac{5}{3}=\dfrac{2}{3}\\\\a_3=\dfrac{2}{3}+\dfrac{5}{3}=\dfrac{7}{3}\\\\a_4=\dfrac{7}{3}+\dfrac{5}{3}=\dfrac{12}{3}=4\\\\a_5=4+\dfrac{5}{3}=\dfrac{12}{3}+\dfrac{5}{3}=\dfrac{17}{3}\\\vdots\\\\\text{The general formula for nth term of an arithmetic sequence}\\\\a_n=a_1+(n-1)d\\\\\text{We have}\ a_1=-1\ \text{and}\ d=\dfrac{5}{3}.\\\\\text{Substitute}\\\\a_n=-1+(n-1)\left(\dfrac{5}{3}\right)=-1+\dfrac{5}{3}n-\dfrac{5}{3}=\dfrac{5}{3}n-\dfrac{3}{3}-\dfrac{5}{3}[/tex]
[tex]\boxed{a_n=\dfrac{5}{3}n-\dfrac{8}{3}}[/tex]
