13-2

Recursive Definitions

Section 13-2 was the second easiest section in chapter 13. The term recursive means to define in the terms of what came before.

Previous term – tn-1
Two terms back – tn-2
….. – tn-3

The two main directions you will follow for this section is to give a recursive definition for a series of numbers and finding a certain number of terms. Let’s try some examples:

Example 1:
Find the 3rd, 4th, 5th, and 6th terms

Tn = 2tn-1 + 7 and t1 = 3

T2 = 2(3) + 7 = 13
T3 = 2(13) + 7 = 33
T4 = 2(33) + 7 = 73
T5 = 2(73) +7 = 153
T6 =2(153) + 7 = 313

Example 2:
Give a recursive definition for

2, 6, 10, 14

Tn = tn-1 + 4

10, 20, 40, 80

Tn = tn-1(2)

Hope everyone had a great Thanksgiving holiday! Now only 2 more weeks and 1 week of exams (unless your exempt) until Christmas holidays! 