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

Solution :Step 1:In this problem we have to find the solution for these recurrence relation, where we given the initial condition.a: let the recurrence relation is given as an = - an-1 with a0= 5Now we starting with initial condition a0 = 5 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= - a1-1 = - a0a1 = - 5a2 = - a2-1 = - a1a2 = - (-5)a2 = 5Now a3 = - a3-1 = - a2a3 = - 5a4 = - a4-1 = - a3 = -(- 5) a4 = 5Clearly we get alternate solutionsSo we can make the nth solution for this recurrence relation.an = (-1)n 5 .