Basic Recurrence Relations

Consider the first 5 terms in the sequence.

98, 97, 96, 95, 94, ...

This can be generated using the recurrence relation:

Consider the following sequence.

24, 36, 54, 81, ...

The terms can be generated using the recurrence relation

Which of the following rules can be used to model this arithmetic sequence?

2, −3, −8, −13, −18…

Which of the following rules can be used to model this geometric sequence?

0.5, 1, 2, 4, 8, …

Match up the following terms with their definition

• produce successive terms in a sequence

• recursion rule

• constant ratio between terms

• recursive relation

• enables you to find the nth term

• arithmetic sequence

• constant difference between terms

• geometric sequence

How many dollars does Julie initially invest?

The first five terms of a sequence are 2, 6, 22, 86, 342.

The recurrence relation that generates this sequence could be:

• $P_0=2\ \ \ \ \ \ \ \ P_{n+1}=P_n\ +\ 4$

• $P_0=2\ \ \ \ \ \ \ \ P_{n+1}=2P_n\ +\ 2$

• $P_0=2\ \ \ \ \ \ \ \ P_{n+1}=3P_n$

• $P_0=2\ \ \ \ \ \ \ \ P_{n+1}=4P_n\ -\ 2$

• $P_0=2\ \ \ \ \ \ \ \ P_{n+1}=5P_n\ -\ 4$

The purchase price of a car was $26 000.
Using the reducing balance method, the value of the car is depreciated by 8% each year.
A recurrence relation that can be used to determine the value of the car after n years,  $C_n$  is

•  $C_n\ =\ 26000,\ \ \ \ \ \ \ C_{n+1}\ =\ 0.92C_n$  

•  $C_n\ =\ 26000,\ \ \ \ \ \ \ C_{n+1}\ =\ 1.08C_n$  

•  $C_n\ =\ 26000,\ \ \ \ \ \ \ C_{n+1}\ =\ C_n+8$  

•  $C_n\ =\ 26000,\ \ \ \ \ \ \ C_{n+1}\ =\ C_n-8$  

•  $C_n\ =\ 26000,\ \ \ \ \ \ \ C_{n+1}\ =\ 0.92C_n-8$  

What is the initial or starting value of the geometric sequence 2, 4, 8, 16,....?

According to the rule to=2, tn+1 = 3tn, what is the value of t1?

Mathematical Equivalence

ON