$(8$ marks$)$ Given the Following recurrence relation:

$T(n)=T(n-1)+n,T(1)=1$

a$)(3$ marks$)$ Suggest a pseudocode for an algorithm whose running time

complexity is described by the given recurrence relation.

b$)(4$ marks$)$ Convert the given recurrence relation into closed form using the

iteration method.

c$)(1$ mark$)$ What is the time complexity $($use Big$-$O notation$)$