4.

a. Give a recursive definition for the following sequence which is defined over the

natural numbers:

2, 6, 18, 54, 162, 486,

b. Use the pseudo code below to formulate an equivalent recursive definition

Function f(n)

if n = 0:

return 1;

else:

return f(n-1)+3n+2;

end

end

c. Using your recursive definition from (5b) compute (3).

d. Find a closed-form solution to the function

e. Prove, by induction, that your closed-form solution in (5d) is correct.

ifn=0 f(n-1) + 2n otherwise 0 f(n) =