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OneDeus2022-01-08 00:47:29
Mathematics
OneDeus, 2022-01-08 00:47:29

How to issue this algorithm in the form of a mathematical formula?

You need to give a formula that, when substituting n, where n is the row number in column X, will match the number in column X
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The most I learned:
Difference between digits X=Xn+Yn
Difference between digits Y=Yn+Zn
Formula for difference between digits Z=(10*(6-n)) for n <= 5 and n > 0
The problem is that it should be n <= 7 and n > 0 and be true for the numbers X1, and it is also known which n1 in X

XYZ
1. ├─150 ├─90 ├─50
2. ├─240 ├─140
├─40 ─180 ├─30
4. ├─560 ├─210 ├─20
5. ├─770 ├─230 └─10
6. ├─1000 └─240
7. └─1240

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2 answer(s)
R
Rsa97, 2022-01-08
@OneDeus

61d8be8ff0284297015450.png

H
hint000, 2022-01-08
@hint000

sum(Z_1:Z_n)=
=sum(Z_1:Z_5)-sum(Z_n+1:Z_5)=
=((Z_1)+(Z_5))*5/2-((Z_n+1)+(Z_5)) *(5-n)/2=
=5n(11-n)
Y_n=
=(Y_1)+sum(Z_1:Z_n-1)=
=(Y_1)+5n(11-n)=
=90+5n(11 -n)
X_n=
=(X_1)+sum(Y_1:Y_n-1)=
=(X_1)+sum[k=1:n-1]((Y_1)+sum(Z_1:Z_k-1))=
= (X_1)+(n-1)*(Y_1)+sum[k=1:n-2](k*Z_k)=
=150+(n-1)*90+sum[k=1:n-2 ](k*Z_k)=
=150+(n-1)*90+10*sum[k=1:n-2](6*kk*k));

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