Find the solution to each of these recurrence relations and initial conditions. Use an iterative approach such as that used in Example 10.

a)

b)

c)

d)

e)

f)

g)

h)

Solution :

Step 1:

In this problem we have to find the solution for these recurrence relation, where we given the initial condition.

a: the recurrence relation is given as

an = 3 an-1 with a0= 2

Now we starting with initial condition a0 = 2 and working upward until we reach an to deduce a closed formula for the sequence. Then

We put n = 0 ,1,2,3,4……...so on , Then

a1= 3a1-1

a1 = 3 a0 = 3.2

a2 = 3a2-1

a2 = 3a1 = 3.3.2 = 32.2

a3 = 3a3-1

a3 = 3a2 = 3.32.2 = 33.2

………..

………..

an = 3an-1 = 3n.2