依题意可知Ai=ai•ai+1,
∴Ai+1=ai+1•ai+2,
若{An}为等比数列则 (Ai+1/Ai)=(ai+2/ai) =q（q为常数）,则a1,a3,…,a2n-1,…和a2,a4,…,a2n,…均是等比数列,且公比均为q；
反之要想{An}为等比数列则 (Ai+1/Ai)=(ai+2/ai) 需为常数,即需要a1,a3,…,a2n-1,…和a2,a4,…,a2n,…均是等比数列,且公比相等；
故{An}为等比数列的充要条件是a1,a3,…,a2n-1,…和a2,a4,…,a2n,…均是等比数列,且公比相同．
故选D