Question

Aight I think I just figured out this pyramidal sequence thing. You're going up by perfect numbers right, like 4, 9, 16, 25. Because all of those are square numbers right? The 4 would be 2, 9 and 3, 16 and 4, 25 and 5... Right? Sorry if I confused you, I have to take my finals plus two other tests tomorrow so I have to go back and re-learn everything(or you know just actually learning it for the first time).

Answer 1

Answer:  Close.  Your observation is correct. When you see that the difference between two numbers in the sequence is a perfect square, you are looking at a pyramidal sequence

1² = 1 top of pyramid

1 + 2² = 5   total in top 2 layers

1 + 2² + 3² = 14 total in top 3 layers

1 + 2² + 3² + 4² = 30 total in the top 4 layers.

1 + 2² + 3² + 4² + 5² = 55  total in the top 5 layers.

Layer 6 is 6² more, 91

Layer 7 is 7² more so, 140

I think you got it.

Step-by-step explanation:  The numbers are like when you keep adding the layers in a pyramid, and the next number is the total of the previous layers plus the square of the next layer number.