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Prob 4. Let {a, } be a sequence of real numbers. The backward differences of this sequence are defined recursively as follows: The first difference Va,, is defined as Van = an - Un-1. The (k + 1)st difference V*+lan is obtained from Vkan by Vitlan = Vkan - Vkan-1. (a) Prove that an & can be expressed in terms of an, Van, ..., Vkan. (b) Show that any recurrence relation for the sequence {a, } can be written in terms of an, Va,, Via,, .... The resulting equation is called a difference equation