Regional math problem for your pleasure

[Anonymous No.11852362]

Given the following array:

[eqn]begin{bmatrix}
1 & 2 & 3 & & & & \\
4 & 5 & 6 & 7 & & & \\
8 & 9 & 10 & 11 & 12 & &\\
13 & 14 & 15 & 16 & 17 & 18 \end{bmatrix}[/eqn]

Find the first element in the hundreth line for this array

[Anonymous No.11852368]

>>11852362
[math]
\begin{bmatrix} 1 & 2 & 3 & & & & \\ 4 & 5 & 6 & 7 & & & \\ 8 & 9 & 10 & 11 & 12 & &\\ 13 & 14 & 15 & 16 & 17 & 18 \end{bmatrix}
[/math]

[Anonymous No.11852369]

>>11852362
matrix*

[Anonymous No.11852377]

>>11852368
3 = 1 + 2 + 3 - 3 elements on the first row, 3 + 4 = 1 + 2 + 3 + 4 - 3 elements on the first two row, 1 + 2 + ... + n - 3 = n(n + 1)/2 - 3 on the first n row. So there are 99(100)/2 - 3 = 4487 elements on the first 99 rows, so the first element on the 100th row is 4488.

[Anonymous No.11852390]

>>11852362
This is trivial, can we talk about race and IQ?

[Anonymous No.11852443]

>>11852377
Wrong, answer is 5149

[Anonymous No.11852495]

>>11852362
is this a programming question?

[El Arcón No.11852498]

>>11852362
Didn't Gauss write the formula for that?

[Anonymous No.11852501]

>>11852495
Nope.
It can be easily verified by a program but the idea is to find an analytic expression for the first element in the 99th row.
I botched the tex but >>11852368
Got it to display properly

[Anonymous No.11853318]

>>11852377
The evaluation of 99(100)/2 - 3 is wrong. It should simplify to 4947 leading to a final answer of 4948. Also you're right >>11852443. It should be the sum of the first n + 2 positive integers as was being calculated in the 2 examples, so 101 should have been substituted for n leading to 101(102)/2 - 3 = 5148 and a final answer of 5149.

[Anonymous No.11853404]

>>11853318
I solved it diferently.
My approach was that clearly the nth row has n+2 elements and that the last element of the nth row is n(n+2)-(missing elements to complete the array)
By missing elements i mean the elements that make it so the last element isnt simply n(n+2).
The number of missing elements in the nth row are clearly [math]\sum_{i=1}^{n-1}i[/math] thus the general expression for the first element in the nth row would be:
[eqn]F_n = n^2 +2n - \Big[ \frac{n(n+1)}{2} - n \Big] + 1[/eqn]

Substitute 99 and you get 5149