Arithmetic and geometric sequences and series

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Arithmetic and geometric sequences and series Chapter 3 Arithmetic and geometric sequences and series

Proof and reasoning

Students studying for IB mathematical studies shouldn’t wear uniform 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?

2, 5, 10, 17, … What’s the next number in the sequence? 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 = 28 What will S5 be?