1 fn is defined recursively by f0 3 and for n 0 1 2 fn

1) f(n) is defined recursively by f(0) = 3 and for n = 0, 1, 2, · · ·, f(n + 1) = 3*f(n) + 7. Find f(1), f(2), f(3), f(4), and f(5).

2) Give a recursive definition of the set of positive odd integers.

Solution

1) f(1) = 3*f(0) + 7, so f(1) = 16

f(2) = 3*f(1)+7, so f(2) = 55

f(3) = 3*f(2)+7, so f(3) = 172

f(4) = 3*f(3)+7, so f(4) = 523

f(5) = 3*f(4)+7, so f(5) = 1576

2)The recursive function for odd integers is, f(0) = 1, f(n+1) = f(n)+2.