Polynomial sequence

Okay kiddo, a polynomial sequence is like a special type of math problem where we start with a certain number and then we add or subtract another number each time to get a new number.

For example, let's say we start with 1, then we add 2 to it to get 3. Then we add 3 to 3 to get 6. And so on. This would be a polynomial sequence because we can write it as a formula using powers of the original number (in this case, 1).

So the formula for our sequence would be:

1, 3, 6, 10, 15...

This formula is called a polynomial because it involves using powers of the original number. Specifically, the formula for this sequence is:

n(n+1)/2

Where n represents the position of the number in the sequence. So the first number (at position 1) is 1, the second number (at position 2) is 3, the third number (at position 3) is 6, and so on.

Pretty cool, right? These types of sequences can be found in all sorts of places in math and science, and they're a lot of fun to play around with!