Why the differences between each number of a $x^2$ sequence is always an odd number and increase by $2$? I'm not a math person at all and I realize that this might be obvious, I'm trying to increase my awareness about it, so please excuse me if the question is too basic.  Also excuse my lack of formatting in expressing my ideas, any tip or correction would be appreciated.
If you square the elements of a sequence of natural numbers $(1, 2, 3, 4,...)$ you respectively get $1,4,9,16,...$ If you calculate the difference between each consecutive element, you get $3,5,7, ...:$
This list of differences would always be composed of odd numbers. Why?
Also, why does it 'grows' linearly, increased by $2$ on every step?
Thanks.

Here is a well known proof without words:

https://steemit.com/math/@ertwro/math-proofs-without-words-visually
