Solve the following recurrence relations using the initial c

Solve the following recurrence relations using the initial condition a_n = 1.

a.) a_n = a_n/2 + d

b.) a_n = 2a_n/2 + d

c.) a_n = 2a_n/2 + dn

Solution

sub an in eq 1

we get

1=a<n/2>+d

in eq 2

we get

1=2a<n/2>+d

solve this equation to get values

and then sub in eq 3 to get n