Download Chapter 3

Chapter 3
Arithmetic and geometric sequences
and series
Proof and reasoning
TOK
Students studying for IB mathematical
studies shouldn’t wear uniform
What reasoning is there that supports or contradicts
this statement?
Can you create a reasoned argument justifying this?
TOK
2, 5, 10, 17, …
• What’s the next number in the sequence?
• Can you explain why?
• Can you prove why?
What is the difference between explaining and proving?
What is important when showing a mathematical proof?
Mathematics is beautiful!
TOK
What is beauty?
From Fibonacci to geometric
Fibonacci sequence
1, 1, 2, 3, 5, 8, 13, 21, …
What happens if you divide one number in the Fibonacci
sequence by the next?
What if you keep going?
At some point, these ratios get very close to forming a
geometric sequence.
At this point, what is r?
From sequence to series
A sequence is a pattern of numbers:
1
5
9
13
17
21
…
A series is what you get when you add the values of the
sequence one by one:
S1 = 1
=1
S2 = 1 + 5
=6
S3 = 1 + 5 + 9
= 15
S4 = 1 + 5 + 9
+ 13
What will S5 be?
= 28