Calculation of the pyramid (Sequence of numerical progressions).
Front side: :   Progress Sums:-1,-2,-3,-4,-5...    1,2,3,4,5... We express the formulas:Sn= (n²a₁+n)/2, ; Sn-1=(n²a₁-n)/2,.  (n - Number of summing members, a₁ -  first member of the progression. With a negative or positive value n. Expressions Sn-1, Sn-2  should be understood: subtraction from the number of the member taken). First option:     Example: Sn= (n²a₁+n)/2. For n = -5 we have: ((-5)2(-1)+(-5))/2=-15;                          For n = 5 we have: (52*1+5)/2=15.    Example: Sn-1=(n²a₁-n)/2  For n = -5 we have: ((-5)2(-1)-(-5))/2=-10                            For n = 5 we have: (52*1-5)/2=10.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Triangular:                                                                                                                                                                                                                  Progress Sums:-1,-3,-6,-10,-15....1,3,6,10,15....                                         We express the formulas:Sn= ((n+a₁)3-(n+a₁))/6, Sn= (n3-n)/6+(n²a₁+n)/2;  Sn-1=(n3-n)/6; Sn-2=((n-a₁)3-(n-a₁))/6,         Sn-2=(n3-n)/6-(n²a₁-n)/2.          First option:       Example: Sn= ((n+a₁)3-(n+a₁))/6.   For n = -5 we have: ((-5+(-1))3-(-5+(-1)))/6=-35;             For n = 5 we have: ((5+1)3-(5+1))/6=35.     Example: Sn-2=((n-a₁)3-(n-a₁))/6.   For n = -5 we have:((-5-(-1) ... Read more

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Calculation of the pyramid (Sequence of numerical progressions).

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