Question: If you are given a sequence a1, a2, a3, . .. then the (discrete) derivative of this sequence is defined to be the new, related

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. a2 - a1, a3 - 02, d4, -93, . ... 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 on = 2n + 1. (3) Find a sequence on whose discrete derivative is the sequence n

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