设数列{Xn}满足logaXn+1=1+logaXn(a>0且a不等于1,a∈N+),且X1+X2+...+X100=100,则X101+X102+...+X200的值A.101a B.101a^2 C.101a^100 D.100a^100

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设数列{Xn}满足logaXn+1=1+logaXn(a>0且a不等于1,a∈N+),且X1+X2+...+X100=100,则X101+X102+...+X200的值A.101a B.101a^2 C.101a^100 D.100a^100
设数列{Xn}满足logaXn+1=1+logaXn(a>0且a不等于1,a∈N+),且X1+X2+...+X100=100,则X101+X102+...+X200的值
A.101a B.101a^2 C.101a^100 D.100a^100

设数列{Xn}满足logaXn+1=1+logaXn(a>0且a不等于1,a∈N+),且X1+X2+...+X100=100,则X101+X102+...+X200的值A.101a B.101a^2 C.101a^100 D.100a^100
1 logaXn+1=1+logaxn
logaXn+1-logaxn=1
loga xn+1/xn=1所以a=xn/xn+1=q
X101+X102+X103+...+X200/X1+X2+X3+...+X100=q^100
所以X101+X102+X103+...+X200=100*q^100=100*a^100
所以选D ,

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