[tex]a_n=\left\{-3,\ -\dfrac{1}{2},\ 2,\ \dfrac{9}{2},\ 7,\ ...\right\}\\\\a_1=-3\\\\a_2=-3+2\dfrac{1}{2}=-\dfrac{1}{2}\\\\a_3=-\dfrac{1}{2}+2\dfrac{1}{2}=2\\\\a_4=2+2\dfrac{1}{2}=4\dfrac{1}{2}=\dfrac{9}{2}\\\\a_5=4\dfrac{1}{2}+2\dfrac{1}{2}=7\\\\\text{The explicit formula of the nth term of the arithmetic sequence:}\\\\a_n=a_1+(n-1)d\\\\d-common\ difference\\\\\text{We have}\ a_1=-3\ \text{and}\ d=2\dfrac{1}{2}=\dfrac{5}{2}.\ \text{Substitute:}[/tex]
[tex]a_n=-3+(n-1)\left(\dfrac{5}{2}\right)=-\dfrac{6}{2}+\dfrac{5}{2}n-\dfrac{5}{2}=\boxed{\dfrac{5}{2}n-\dfrac{11}{2}=\dfrac{5n-11}{2}}[/tex]
