$($Answer must be in your own hand$-$writing. Affix your signature

in each page of your answer.$)$

$($a$)$ Solve the recurrence relation: $a_{n+1}-a_n=3n,n0,a_0=1.$ Obtain the

generating function of $a_n.$

$\%$

$(4$ marks$)$

$($b$)$ Solve the recurrence relation: $a_{n+2}-11a_{n+1}+24a_n=0,a_0=1,a_1=2.$

$\%$

$(3$ marks$)$