已知数列{an}是等差数列,数列{bn}满足bn=(1/2)^an已知数列{an}是等差数列,数列{bn}满足bn=(1/2）^an,b1+b2+b3=21/8,b1*b2*b3=1/8,求数列{an}的通项

Question

已知数列{an}是等差数列,数列{bn}满足bn=(1/2)^an
已知数列{an}是等差数列,数列{bn}满足bn=(1/2）^an,b1+b2+b3=21/8,b1*b2*b3=1/8,求数列{an}的通项

Answer 1

B(n+1)/Bn=(1/2)^A(n+1)/(1/2)^An=(1/2)^(A(n+1)-An)=(1/2)^d
{Bn}是等比数列
B1×B3=(B2)^2
B1×B2×B3=(B2)^3=1/8
B2=1/2
B1=B2/q=1/(2q)
B3=B2×q=q/2
B1+B2+B3=1/(2q)+1/2+q/2=21/8
4q^2-17q+4=0
q=4或q=1/4
B2=(1/2)^A2=1/2
A2=1
当q=4时,q=(1/2)^d=4
d=-2
A1=A2-d=1-(-2)=3
An=A1+(n-1)d=3+(n-1)×(-2)=5-2n
当q=1/4时,q=(1/2)^d=1/4
d=2
A1=A2-d=1-2=-1
An=A1+(n-1)d=-1+(n-1)×2=2n-3