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?

Question

Bright Tutorials · Accepted Answer

When you start to add up hexagonal numbers, you obtain a sequence of cubic numbers.
Let’s add them up cumulatively:
1. Sum of first hexagonal number: 1
2. Sum of first two hexagonal numbers: 1 + 7 = 8
3. Sum of first three hexagonal numbers: 1 + 7 + 19 = 27
4. Sum of first four hexagonal numbers: 1 + 7 + 19 + 37 = 64
This sequence is 1, 8, 27, 64,…..
The sequence 1, 8, 27, 64,…. is the sequence of cubic numbers: 13, 23, 33, 43, 53,…..
The cube number: C
n
= n
3

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