What happens when you start to add up hexagonal numbers? Can you explain it using a picture of a cube?

What happens when you start to add up hexagonal numbers? Can you explain it using a picture of a cube? Class 6

Question 1.

What happens when you start to add up hexagonal numbers, i.e., take 1, 1 + 7, 1 + 7 + 19, 1 + 7 + 19 + 37, … ? Which sequence do you get? Can you explain it using a picture of a cube? Class 6

Solution:

We get 1, 8, 27, 64, ...

It is a sequence of cube numbers.

Using the above first picture of the cube, it can be explained.

Question 2.

Find your own patterns or relations in and among the sequences in Table 1. Class 6

Can you explain why they happen with a picture or otherwise?

Solution:

Do as directed.