Question

设{xn}是各项都为正数的等比数列,{yn}是等差数列,且x1=y1=1,x3+y5=13,x5+y3=21

Answer 1

{yn}公差d,{xn}公比q

xn=q^(n-1)

yn=1+(n-1)*d

解方程：

q^2+4d+1=13;

q^4+2d+1=21;

下式*2-上式得到2*q^4-q^2+1=29; =>q^2=4,q取正的,q=2,d=2

于是xn=2^(n-1),yn = 2n-1;