若数列{xn}满足lgxn+1=1+lgxn,且x1+x2+…+x100=100,则lg(x101+x102+…+x200)=(  ) A.102 B.100 C.1000 D.101

问题描述:

若数列{xn}满足lgxn+1=1+lgxn,且x1+x2+…+x100=100,则lg(x101+x102+…+x200)=(  )
A. 102
B. 100
C. 1000
D. 101

∵lgxn+1=1+lgxn
∴lgxn+1-lgxn=1,∴lg

xn+1
xn
=1,
∴lg(x101+x102+…+x200
=lg[(x1+x2+…+x100)×10100]
=lg(100×10100
=lg10102
=102
故选:A.