for every ipteger n > 0. Show that Let d, d , d , . be defined by the formula d = 0 1 2 3 this sequence satisfies the following recurrence relation for every integer k 2 2| d̟ = 5d, -1- 6d̟ - 2 2.

A sequence a,,a, ,az,..., satisfies the recurrence relation a, = 3a +10a2, with initial conditions a, = 5 and a, = 8. Find an explicit formula for the sequence. Use this formula to calculate a,0. %3D %3D

Write a recurrence relation and initial conditions for the number Sn of sequences of Nickles, dimes and quarters that can be inserted into a vending machine to purchase a soft drink costing 5n cents. How many sequences are there for a drink costing 50 cents?

Find a recurrence relation for the number of sequences of yellow and purple stones of length N, where each sequence has the property that no two adjacent stones are purple. HINT: Treat sequences whose final stone is yellow separately from sequences whose final stone is purple.