Solve the following recurrence relations. You may use any method discussed in class, but you need to justify your answers by showing all relevant details. If you use a guess$-$and$-$prove method, remember to prove the correctness of your guess.

a$.$

$T(n)=\{\begin{array}{ccc}1& \text{f}\text{o}\text{r}& n=1\\ T(n-1)+2& \text{f}\text{o}\text{r}& n2\end{array}$

b$.$

$T(n)=\{\begin{array}{ccc}1& \text{f}\text{o}\text{r}& n=1\\ 3T(\frac{n}{2})+n^2& \text{f}\text{o}\text{r}& n2\end{array}$