The sequence {a} begins with 2, 1,-1, -2, -1, 1, 2, ... n From the list below select a recurrence relation and initial conditions that define the given sequence. {a}: 2, 1, 1, -2, -1, 1, 2, ... n O a = 2, a₁ = 1, a = a₁ 1 n O a = 3, a₁ = -1, a = a 1 n n-1 a=2, a₁ = 1, -an-2 + a n-2 n-1 a=2, a₁ =1, a a .a n n-2 n-1 a = a n n-2-an-1

Determine if the sequence {b„} is a solution to the recurrence relation an = 2an-1 + 3an-2, Vn > 2. %3D a) bn = 3n+1, Vn > 0 b) bn = n+1, Vn > 0 %3D %3D

Give a recurrence relation that would fit the sequence a1, az, A3, A4, A5, .= 1,2, 5, 26, 677 ...

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?