(Solved): 4. (4 marks) Consider the following algorithm. The time complexity of this algorithm is given by t ...

4. (4 marks) Consider the following algorithm. The time complexity of this algorithm is given by the following recurrence equation: \[ \begin{aligned} f(1) &=c_{0} \\ f(n) &=f(n-1)+c_{1} n+c_{2}, \text { for } n>0 \end{aligned} \] where \( c_{0}, c_{1} \), and \( c_{2} \) are constants. Solve the recurrence equation using repeated substitution and give the order of \( f(n) \). You must explain how you solved the equation.