如果数列{an}是等差数列,设bn=(1/2)^an,数列{bn}是等比数列吗?

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$如果数列{an}是等差数列,设bn=(1/2)^an,数列{bn}是等比数列吗?$

数列{an}是等差数列,设公差为d,
则an-a(n-1)=d(常数)
bn=(1/2)^an,
则bn/b(n-1)=[ (1/2)^an]/[ (1/2)^a(n-1)]
=(1/2)^(an- a(n-1))= (1/2)^d
因为d是常数,所以(1/2)^d是常数,
∴数列{bn}是等比数列.

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