Consider the Recurrence Relation $$a _ { n } = 3 a _ { n - 1 } + 5 ^ { n }$$

Consider the recurrence relation $$a _ { n } = 3 a _ { n - 1 } + 5 ^ { n }$$ (a) Write the associated homogeneous recurrence relation.
(b) Find the general solution to the associated homogeneous recurrence relation.
(c) Find a particular solution to the given recurrence relation.
(d) Write the general solution to the given recurrence relation.
(e) Find the particular solution to the given recurrence relation when a0 = 1.