13-2

13-2
Section 13-2 was about recursive definitions. Recursive means define in terms of what came before.
tn-1: previous term
tn-2: two terms back
tn-3: …
EXAMPLE 1: tn=3tn-1 + 1 and tn=6. Find the 3, 4, and 5 terms.
A). t2=3(6) + 1 = 19
t3=3(19) + 1 = 58
t4=3(58) + 1 = 175
t5=3(175) + 1 = 526
B). 58, 175, and 526 are your 3, 4, and 5 terms. All you do is replace tn-1 with tn to begin. Then you take your answer and place is where tn-1 is each time.

EXAMPLE 2: Give a recursive definition for 6, 10, 14, 16..
A). Looking at the numbers above, you can easily see that you’re adding 4 each time to make this arithmetic pattern.
B). Your recursive definition is tn=tn-1 +4

Hope everyone had a great, relaxing Thanksgiving break :)