Question

數列{a_n}為等比數列,且滿足a₂₀₀₇+a₂₀₁₀+a₂₀₁₆=2,a₂₀₁₀+a₂₀₁₃+a₂₀₁₉=6,則a₂₀₀₇+a₂₀₁₀+a₂₀₁₃+a₂₀₁₆+a₂₀₁₉等于（ ）

A．

B．

C．

D．

Answer 1

C

易得a_{2 007}(1+q³+q⁹)=2,a_{2 010}(1+q³+q⁹)=6,兩式相除,得到==,得q³=3,將其代入a_{2 010}(1+q³+q⁹)=6,得a_{2 010}=,故所求為(a_{2 007}+a_{2 010}+a_{2 016})+(a_{2 010}+a_{2 013}+a_{2 019})-a_{2 010}=2+6-a_{2 010}=.故選C