Question

设a1=2,数列{1-2an}是公比为2的等比数列,则an=＿＿＿＿＿＿.

Answer 1

数列{1-2an}是公比为2的等比数列:

1-2an=(1-2a1)*2^(n-1)

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

1-2an=-3*2^(n-1)

2an=3*2^(n-1)+1

an=3*2^(n-2)+1/2