Question 9 - Relations among Number Sequences - Chapter 1 Class 6 - Patterns in Mathematics (Ganit Prakash)

Transcript

Question 9 Find your own patterns or relations in and among the sequences in Table 1. Can you explain why they happen with a picture or otherwise? 1, 1, 1, 1, 1, 1, 1, ... 1, 2, 3, 4, 5, 6, 7, ... 1, 3, 5, 7, 9, 11, 13, ... 2, 4, 6, 8, 10, 12, 14, ... 1, 3, 6, 10, 15, 21, 28, ... 1, 4, 9, 16, 25, 36, 49, ... 1, 8, 27, 64, 125, 216, ... 1, 2, 3, 5, 8, 13, 21, ... 1, 2, 4, 8, 16, 32, 64, ... 1, 3, 9, 27, 81, 243, 729, ... (All 1’s) (Counting numbers) (Odd numbers) (Even numbers) (Triangular numbers) (Squares) (Cubes) (Virahānka numbers) (Powers of 2) (Powers of 3) Pattern found: Take the Square Numbers and find the difference between each pair. From Table 1: Square Numbers: 1, 4, 9, 16, 25, 36, ... Now subtract: 4 − 1 = 3 9 − 4 = 5 16 − 9 = 7 25 − 16 = 9 36 − 25 = 11 The sequence formed is 3, 5, 7, 9, 11, …. Which are odd numbers Thus, we can say Sequence of Difference in squares gives odd numbers sequence: