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) ...
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