Question 3 - Relations among Number Sequences - Chapter 1 Class 6 - Patterns in Mathematics (Ganit Prakash)

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Question 3 Which sequence do you get when you start to add the All 1’s sequence up? What sequence do you get when you add the All 1’s sequence up and down?The All 1’s sequence is: 1, 1, 1, 1, 1, ... When we add up the All 1’s sequence, we get: 1 1 + 1 = 2 1 + 1 + 1 = 3 1 + 1 + 1 + 1 = 4 1 + 1 + 1 + 1 + 1 = 5 ...and so on. This gives the Counting Numbers sequence: 1, 2, 3, 4, 5, … When we add the All 1’s sequence up and then down, like: When up and down, it means one central number, and one on each sides. Similarly, one central number, and two on each sides And so on… Thus, it looks like 1 1 + 1 + 1 = 3 1 + 1 + 1 + 1 + 1 = 5 1 + 1 + 1 + 1 + 1 + 1 + 1 = 7 This gives the Odd Numbers sequence: 1, 3, 5, 7, 9, … Thus, Adding up All 1’s → Counting Numbers Adding up and down All 1’s → Odd Numbers