杭州交通信息网自制红薯粉皮制作过程:数列问题1
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设Sn是等差数列an前n项和,若a5/a3=5/9则s9/s5=什么
a5/a3 = 5/9
a5 = 5k
a3 = 9k
a5 - a3 = -4k = 2d ......... d = -2k
a3 = a1 + 2d = 5k........................这步代入错误，该是9k
a1 = 5k - 2d = 9k
an = a1 + (n - 1)d = 9k - 2(n - 1)k
Sn
= (a1 + an)*n/2 = [9 + 9 - 2(n - 1)]*k*n/2
= (10 - n)n*k
则s9 = 9k、s5 = 25k
S9/S5 = 9/25
补充——注意：推导错误，看别人的答案吧。
a5=a1+4d...1
a3=a1+2d...2
1式除以2式为5/9
a1=-13d/2
sn=n*a1+n*(n-1)d/2...3
1式和2式代入3式得：
s9:s5=1
-3/5