91Ó°ÊÓ

Tell whether or not each recurrence relation in Exercises \(1-10\) is a linear homogeneous recurrence relation with constant coefficients. Give the order of each linear homogeneous recurrence relation with constant coefficients. \(a_{n}=-3 a_{n-1}\)

Describe how the closest-pair algorithm finds the closest pair of points if the input is \((8,4),(3,11),(12,10),(5,4),(1,2),\) \((17,10),(8,7),(8,9),(11,3),(1,5),(11,7),(5,9),(1,9),(7,6),(3,7),(14,7).\)

In Exercises \(1-3\), find a recurrence relation and initial conditions that generate a sequence that begins with the given terms. $$ 3.7,11,15, \ldots $$

In Exercises \(1-3\), find a recurrence relation and initial conditions that generate a sequence that begins with the given terms. $$ 3,6,9,15,24,39 \ldots $$

What can you conclude about input to the closest-pair algorithm when the output is zero for the distance between a closest pair?

Tell whether or not each recurrence relation in Exercises \(1-10\) is a linear homogeneous recurrence relation with constant coefficients. Give the order of each linear homogeneous recurrence relation with constant coefficients. \(a_{n}=2 n a_{n-1}\)

In Exercises \(1-3\), find a recurrence relation and initial conditions that generate a sequence that begins with the given terms. $$ 1,1,2,4,16,128,4096, \ldots $$

Explain why in some cases, when dividing a set of points by a vertical line into two nearly equal parts, it is necessary for the line to contain some of the points.

Tell whether or not each recurrence relation in Exercises \(1-10\) is a linear homogeneous recurrence relation with constant coefficients. Give the order of each linear homogeneous recurrence relation with constant coefficients. \(a_{n}=a_{n-1}+n\)

In Exercises \(4-8,\) assume that a person invests \(\$ 2000\) at 14 percent interest compounded annually. Let \(A_{n}\) represent the amount at the end of \(n\) years. Find a recurrence relation for the sequence \(A_{0}, A_{1}, \ldots\)