I can see the first entry of each row is added to an increase of 1. So 2 = 1+1, 4 = 2+2, 7 = 4+ 3, etc.
So I know that the 64th entry is $x_{64} = x_{63}+63$ But I am stuck on how to calculate it.
And If I wanted to find the sum of all the entries up until the 2018th row, would it be $\frac{n(n+1)}{2}$? That is what I've been seeing for triangular numbers however the difference is that these entries are symbolized by actual numbers and not dots.
Additionally, if I wanted to find the "middle" number, I can see that in row 3, it's 5, row 5, its 13, etc. SO each entry is going up by 4, i.e.: 5 = 4+1, 13 = 5+ 8, etc, so how can I calculate the 101st middle number?
Any help is appreciated, thank you!
The first element of the $n$ th row will be $\frac{n(n-1)}{2}+1$, since it will be the sum of all diferences plus 1, then if you want the $k$ the element of the $n$ th row it will be $\frac{n(n-1)}{2}+k$