CBSE Class 6 Mathematics Question 22 of 25

Patterns in Mathematics — Question 24

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24
Question
Count the number of lines in each shape in the sequence of complete graphs. Which number sequence do you get? Can you explain why?
Answer

The number of lines in each shape in complete graphs is 1, 3, 6, 10, 15, …..
This sequence is of triangular numbers.
Why does this happen? The number of edges in a complete graph with n vertices is given by \(\frac{n(n+1)}{2}\)
This formula calculates how many ways you can choose 2 vertices out of n to form an edge, which is essentially the number of unique pairs of vertices.