Question 1 - Think & Reflect (Page 174) - Definition - Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress

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Question 1 - Think & Reflect (Page 174) Can you describe the pattern in each of the above sequences? Can you predict the next few numbers in these sequences? Let’s look at them one by one Natural Numbers (1, 2, 3, 4, 5, 6, …) Here, Pattern – Pattern is that each new term is +1 of previous term Next few terms – Adding 1 to each new term, our next few terms would be 7, 8, 9… Odd Numbers (1, 3, 5, 7, 9, 11, …) Here, Pattern – Pattern is that each new term is +2 of previous term Next few terms – Adding 2 to each new term, our next few terms would be 13, 15, 17… Triangular Numbers (1, 3, 6, 10, 15, 21, 28 …) Here, Pattern – The difference between terms keeps increasing by 1. We add 2, then add 3, then add 4, then add 5, and so on Next few terms – Following the same pattern, our next few terms would be 28 (which is 21 + 7), 36 (which is 28 + 8), 45 (which is 36 + 9) Square Numbers (1, 4, 9, 16, 25, 36, 49, …) Here, Pattern – These are the squares of the natural numbers (12, 22, 32, 42, etc.) Next few terms – Squaring the terms, our next few terms would be 49 (which is 72), 64 (which is 82), 81 (which is 92)