Question

a,b,c成等比数列,a,x,b成等差数列,b,y,c也成等差数列,求a/x+c/y的值?

Answer 1

假设 a/b=b/c=k 则 b=ck,a=ck^2

因为a,x,b成等差数列,b,y,c也成等差数列,所以

x=(a+b)/2 y=(b+c)/2

所以

a/x+c/y

=2a/(a+b)+2c/(b+c)

=2ck^2/ (ck^2+ck)+2c/(ck+c)

=2ck^2/(ck)(k+1) +2c/c(k+1)

=2k/(k+1)+ 2/(k+1)

=(2k+2)/(k+1)

=2