1. In predicting future sales of a product, one assumption is to say that the amount sold next year will be the average of the amount sold this year and last year. Suppose that
an is the amount sold in year n.
(a) Find a recurrence relation for an.
(b) Solve the recurrence relation if a0 = a1 = 1.
What i have found so far is that "an = 2an+1 - an-1"
AM I ON THE RIGHT TRACK? PLEASE HELP ASAP!
I tried solving this recurrence relation, and i got two roots x=1, x= -1/2
then i wrote it in the general form of the solution as:
for some constants A and B.
Then by substituting the given initial values and solving equations, i got A= 1, B=0
So according to this the solution should be, .
Does it make sense? Can i have a solution of the form which means that solution is always 1?
Please reply back asap!