Known: in the arithmetic sequence {an}, A3 + A4 = 15, a2a5 = 54, tolerance d < 0 Find the maximum value of [Sn - (an-3)] / N and the corresponding value of n Ans:n=4 In this case, ymax = 15 / 2 | Math enthusiast | Mathematical art

Known: in the arithmetic sequence {an}, A3 + A4 = 15, a2a5 = 54, tolerance d < 0 Find the maximum value of [Sn - (an-3)] / N and the corresponding value of n Ans:n=4 In this case, ymax = 15 / 2

Because da5, A2 + A5 = A3 + A4 = 15, we get A2 = 9, A5 = 6, d = - 1 from Veda's theorem
Because an is an arithmetic sequence with tolerance 1, so an = 11-n
Sn=(10+11-n)*n/2=(21-n)*n/2=-1/2n^2+21n/2
An-3=11-（n-3)=14-n
[Sn - (an-3)] / N = - (1 / 2) n + 23 / 2-14 / N = 23 / 2 - [(1 / 2) n + 14 / N] take the maximum value when n is 2 times the root 7,
Because n is a positive integer, n = 5 or 6. When n = 5, ymax = 31 / 5
It seems that there are some mistakes in the answer. When n = 4, A1 = 10, A2 = 9, A3 = 8, A4 = 7
Sn=34 ,an-3=a1=10 ,Sn-A(n-3)/n=(34-10)/4=6

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