Question

{an}为以2为首项,-1为公差的等比数列,令bn=(1/2)的an次方,证{bn｝为等比数列并求｛bn｝的通项公式.

Answer 1

{an}为以2为首项,-1为公差的等比数列

an=2-1（n-1)=-n+3

bn=(1/2)的an次方

=(1/2)^(3-n)

b(n-1)=(1/2)^(4-n)

bn/b(n-1)

=(1/2)^(3-n-4+n)

=(1/2)^(-1)

=2

∴bn是等比数列

公比=2

b1=(1/2)^2

∴bn=(1/2)^2*2^(n-1)

=(1/2)^2*(1/2)^(1-n)

=(1/2)^(3-n)