/sci/ - Science & Math » Thread #11852362

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Regional math problem for your pleasure

Anonymous Tue 30 Jun 04:43:23 2020 No.11852362 View Reply Original Report

Quoted By: >>11852368 >>11852369 >>11852390 >>11852495 >>11852498

Given the following array:

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

Find the first element in the hundreth line for this array

Anonymous

Anonymous Tue 30 Jun 2020 04:49:53 No.11852368 Report

Quoted By: >>11852377 >>11852501

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

Anonymous

Anonymous Tue 30 Jun 2020 04:50:27 No.11852369 Report

Quoted By:

>>11852362
matrix*

Anonymous

Anonymous Tue 30 Jun 2020 04:54:47 No.11852377 Report

Quoted By: >>11852443 >>11853318

>>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

Anonymous Tue 30 Jun 2020 05:00:54 No.11852390 Report

Quoted By:

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

Anonymous

Anonymous Tue 30 Jun 2020 05:42:09 No.11852443 Report

Quoted By: >>11853318

>>11852377
Wrong, answer is 5149

Anonymous

Anonymous Tue 30 Jun 2020 06:13:38 No.11852495 Report

Quoted By: >>11852501

>>11852362
is this a programming question?

El Arcón

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El Arcón Tue 30 Jun 2020 06:15:44 No.11852498 Report

Quoted By:

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

Anonymous

Anonymous Tue 30 Jun 2020 06:16:58 No.11852501 Report

Quoted By:

>>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

Anonymous Tue 30 Jun 2020 13:14:14 No.11853318 Report

Quoted By: >>11853404

>>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

Anonymous Tue 30 Jun 2020 13:53:00 No.11853404 Report

Quoted By:

>>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 $\sum_{i=1}^{n-1}i$ thus the general expression for the first element in the nth row would be:
$F_n = n^2 +2n - \Big[ \frac{n(n+1)}{2} - n \Big] + 1$

Substitute 99 and you get 5149

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