Recurrence Relations

Question 1

Consider the solution of given recurrence relation an + 7an–1 + 10an–2 = 0 where a0 = 2 & a1 = 3 by second order linear homogenous recurrence relations:

Answer 1

an = 13/3 (-2)^n + -7/5 (-5)^n

Question 2

What is the general form of first order recurrence relation?

Answer 2

xn = cxn–1

Question 3

The relation defined as Xn+1 = Xn + Xn–1 is named as .

Answer 3

Fibonacci numbers

Question 4

Which among the following is a recurrence relation that defines the nth term in terms of the previous two terms?

Answer 4

Second order recurrence relation

Question 5

Which among the following is an equation that characterises a sequence based on a principle that gives the next term as a relation with previous terms?

Answer 5

Recurrence relation

Question 6

Classify the following as first order linear recurrence relation:

Answer 6

xn = 5xn–1

Question 7

he recurrence relation of the form Xan + Yan–1 + Zan–2 = 0 where X, Y & Z are

Answer 7

Real

Question 8

Consider the solution of following equation by characteristic root method: xn = 3xn–1, x0 = 1

Answer 8

xn = 1.3n

Question 9

Determine the recurrence relation for the following function by iteration method: xn = 4xn–1, x0 = .2

Answer 9

xn = 4xn–1 = 4n-1.2

Question 10

How many methods are used to solve a first order recurrence relation?

Answer 10

2