20 12 Sichuan liberal arts mathematics multiple-choice questions 12 entitled what d to choose? The function f (x) = (x-3) 3+x- 1, the arithmetic progression of the sequence An is known, and the arithmetic difference is not zero. F (A 1)+F (A2)+...+F (A7) Use 1 and 7 terms to get (a1+a7-6) [(a1-3) 2+(a7-3). 0 always saves the combination of items 2 and 6 until the fourth item.

From one to arithmetic series.

(A 1-3)+(A2-3)+...(A7-3)=7*(A4-3)

The following equation can be obtained from the condition A 1)+F (A2)+ ... +F (A7) = 14.

(a4-3)){(a 1-3)^2+(a7-3)^2-(a 1-3)*(a7-3)]+[(a2-3)^2+(a6-3)^2-(a2-3)*(a6-3)]+...+(A4-3)^2+7/2}=0

Since the second factor is always greater than 0, we can get A4=3.