C1 = -5, Cn = 5cn–1 – 3: -5 -5 8

If a sequence is unbounded, then it diverges. True or False?

Let a_n be the number of graphs in which the degree of each vertex is 2 and the number of vertices is n. Find the exponential generating function of the sequence a_n

Find a recurrence relation with initial condition that uniquely determine the sequence 6, -18, 54, -162, ... 2014

Find a closed form for the infinite arithmetic sequence given by the recurrence system:  x1 = -1, xn = xn-1 - 3/2      (n = 2,3,4...)  The closed form is xn =

discrete math

Consider the rabbit pairs that illustrate the pattern in the Fibonacci sequence. These rabbits produce exactly 1 pair of new rabbits after reaching maturity at age 2 months. Imagine that the rabbits and all their offspring live forever. Also, imagine the field the rabbits live in can expand in size so that its side length is exactly equal to the number of pairs of rabbits living in the field. What is the side length of the field at the end of two years? Explain and show your work.

Let (a_n) be the sequence defined by the recursive relation a_n=a_(n−1)+5n+1, with initial term a0=0.Use iteration to find a closed formula for the sequence. Simplify your answer whenever possible.

Find an  for the sequence 1/1 -22/2x1 +33/3x2x1 - 44/4x3x2x1, +...