The growth of the series is arithmetic progression (that is, the series with equal growth), then the series is a quadratic function; If the increase of the series is arithmetic progression, then the series is a cubic function ... and so on. This is the knowledge of series.
As for this question,
5-2=3
10-5=5
17- 10=7
……
an-a(n- 1)=2n- 1
Ann (No.N)
These formulas add up left and right.
Available an-2 = 3+5+7+...+2n- 1.
Note T = 3+5+7+...+2n- 1. Obviously, t is the total increment.
By the way, let me tell you about Gaussian algorithm. After all, this topic should not be in junior high school.
3+5+7+...+2n- 1
2n- 1+2n-3+2n-5+...+3 (reverse writing)
Then add the items, and the corresponding sum of each item is the same number 3+2n- 1, which is the sum of the first item and the last item.
Then 2T=(3+2n- 1)(n- 1).
N- 1 is the total number of terms of t.
So the total increase is t = [3+(2n-1) ]× (n-1) ÷ 2, which is how it came about. . .