Question 5 - Relations among Number Sequences - Chapter 1 Class 6 - Patterns in Mathematics (Ganita Prakash)

Transcript

Question 5 What happens when you add up pairs of consecutive triangular numbers? That is, take 1 + 3, 3 + 6, 6 + 10, 10 + 15, … Which sequence do you get? Why? Can you explain it with a picture?The Triangular Numbers sequence: 1, 3, 6, 10, 15, 21, … We are adding pairs of consecutive triangular numbers: 1 + 3 = 4 3 + 6 = 9 6 + 10 = 16 10 + 15 = 25 15 + 21 = 36 This gives the Square Numbers sequence: 4, 9, 16, 25, 36, ... → which are 2², 3², 4², 5², 6², ... Each triangular number can be drawn as a triangle made of dots. If you take two consecutive triangular numbers, and combine them cleverly, they form a square! Example: Let’s add 3 + 6 = 9