Question

（2011•樂(lè)山一模）公差不為0的等差數(shù)列{a_n}中，4a2011-a20122+4a2013=0，數(shù)列{b_n}是等比數(shù)列，且b₂₀₁₂=a₂₀₁₂，則b₂₀₁₀•b₂₀₁₄=（　　）

A．8

B．32

C．64

D．128

Answer 1

分析：先利用等差數(shù)列的性質(zhì)化簡(jiǎn)等式，再利用等比數(shù)列的性質(zhì)，即可求得b₂₀₁₀•b₂₀₁₄的值．

解答：解：∵等差數(shù)列{a_n}中，4a2011-a20122+4a2013=0
∴8a2012-a20122=0
∵數(shù)列{b_n}是等比數(shù)列，且b₂₀₁₂=a₂₀₁₂，
∴b₂₀₁₂=a₂₀₁₂=8
∴b₂₀₁₀•b₂₀₁₄=b₂₀₁₂²=64
故選C．

點(diǎn)評(píng)：本題考查等差數(shù)列與等比數(shù)列的性質(zhì)，考查學(xué)生的計(jì)算能力，解題的關(guān)鍵是掌握等差數(shù)列與等比數(shù)列的性質(zhì)．