题目

已知等差数列{an}满足an=40-4n,求前多少项的和最大,最大值是多少

提问时间：2021-02-16

答案

a1 = 40 -4 *1 = 36
d = an - an-1 = (40 -4n ) - (40 -4(n-1)) = -4
Sn =n a1 + (d+(n-1)d) *(n-1)/2 =36n -2n(n-1)= -2n^2 + 38n
= -2(n^2 - 19n + 19^2/4) + 19^2/2
= -2(n-19/2)^2 + 19^2/2
n=9或10时(n-19/2)^2= 1/2^2 = 1/4
Sn有最大值 -2 * 1/4 + 19^2/2 = -1/2 + 361/2 = 180