Sequences and Recurrence relations

Question 1

Un+1 = ?

Answer 1

Un+1 = aUn + b

Question 2

Explain why this is a sequence has a limit?

Answer 2

Limit exists when -1 < |a| < 1

Question 3

+ b = ?

- b = ?

Answer 3

+ b = increase

- b = decrease

Question 4

Limit L is equal to …

Answer 4

Limit L is equal to

L = b
——
1 - a

Question 5

In the equation for limit the following suggest:
a = ?
b = ?
Un =?

Answer 5

a = sets limit
b = moves limit
Un = no effect
on limit

Question 6

1. Given three value in a sequence e.g. U10 , U11 , U12 we can work out recurrence relation how?
2. Using what method

Answer 6

1. U11 = aU10 + b
   U12 = aU11 + b
2. Simultaneous equations

Question 7

Recurrence Relations

Answer 7

next number depends on the previous number

Question 8

what is a linear recurrence? 2 ways

Answer 8

U n+1 = au n + b
a = 0

OR

un = au n-1 + b