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Question: a write out the first few terms of the sequence...

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a) Write out the first few terms of the sequence given by a1=3; an=2an-1+4. Then find a recursive definition for 10, 24, 52, 108, ... .

b) Show that an=2n-5n is a solution to the recursion an=7an-1-10an-2. What would the initial conditions need to be for this to be the closed formula for the sequence?

c) Use summation (\sum) notion to rewrite 1+5+9+13+...+425.

d) Find a closed formula for the sequence with recursive definition an=2an-1-an-2 with a1=1 and a2=2.

e) Suppose you draw n lines in the plane. What is the maximum number of regions (call the regions Rn) that can be created, including unbounded regions? Find a recursive formula for the number of regions created by the n lines and justify your answer. Also guess at a closed formula based on your data table.

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