Question

若a,b,c为等差数列,b,c,d为等比数列,1/c,1/d,1/e为等差数列,则a,c,e成?

Answer 1

2b = a+c.

c^2 = bd = (a+c)d/2,2/d = (a+c)/c^2

2/d = 1/c + 1/e = (a+c)/c^2 = a/c^2 + 1/c,

1/e = a/c^2,

c^2 = ae

a,c,e 成等比数列.