等差数列{An}中,公差不等于0,已知S100=100S10,则A100/A10=?

Question

等差数列{An}中,公差不等于0,已知S100=100S10,则A100/A10=?

Answer 1

答案：199/19
解析：
S100=(100(A1+A100))/2
A100=A1+99D
S100=(100A1+100A1+9900D)/2=(200A1+9900D)/2
S10 =( 10(A1+ A10))/2
A10 =A1+ 9D
S10 =(10A1+10A1+90D)/2=(20A1+90D)/2
因为：
s100=100s10
所以：
(200A1+9900D)/2=100(20A1+90D)/2
200A1+9900D=2000A1+9000D
1800A1=900D
A1=0.5D
A100=A1+99D=99.5D
A10 =A1+ 9D=9.5D
A100/A10=99.5/9.5=199/19