Question

記等比數(shù)列{a_n}的前n項(xiàng)積為，已知a_m-1a_m+1-2a_m=0，且T_2m-1=128，則m=    ．

Answer 1

【答案】分析：由a_m-1a_m+1-2a_m=0，結(jié)合等比數(shù)列的性質(zhì)可得，，從而可求a_m=2，而T_2m-1=a₁a₂…a_2m-1=（a₁a_2m-1）•（a₂a_2m-2）…a_m==2^2m-1，結(jié)合已知可求m
解答：解：∵a_m-1a_m+1-2a_m=0，
由等比數(shù)列的性質(zhì)可得，
∵a_m≠0
∴a_m=2
∵T_2m-1=a₁a₂…a_2m-1=（a₁a_2m-1）•（a₂a_2m-2）…a_m
===2^2m-1=128
∴2m-1=7
∴m=4
故答案為4
點(diǎn)評(píng)：本題主要考查了等比數(shù)列的性質(zhì)：若m+n=p+q，則a_m•a_n=a_pa_q的應(yīng)用，屬于基礎(chǔ)試題