Question 2. There are many parallels between sequences and functions. In this question you will explore the "discrete derivative" which is a way to describe the growth rate of a sequence. If you are given a sequence a1, a2, a3, . . . then the (discrete) derivative of this sequence is defined to be the new, related sequence of successive differences between terms. i.e. d2 - Q1, a3 - Q2, a4, -03, . . .. For example, the (discrete) derivative of the sequence 1, 10, 100, 1000, . .. is 9, 90, 900, 9000, . ... (1) Find the discrete derivative of the sequence 1, 4, 9, 16, 25, . ... Write this derivative in the form an = [ something ]. (2) Find the discrete derivative of the sequence bn = 2n + 1. (3) Find a sequence on whose discrete derivative is the sequence n. (4) Find a sequence dn whose discrete derivative is the same sequence dn itself. (Hint: Use your intuition about functions and derivatives #:3:85. You may need to play around and experiment to find such a sequence. ) (5) Briefly explain how discrete derivatives are related (or unrelated) to the (standard) derivatives of functions we studied