若数列{an}中,a1=10,an+1=根号an(n∈n),则数列{an}的通项an=

Question

若数列{an}中,a1=10,an+1=根号an(n∈n),则数列{an}的通项an=

Answer 1

an+1=√an,两边取常用对数,得：lgan+1=1/2lgan,即{lgan}是公比为1/2的等比数列,
所以lgan=(1/2)^(n-1),an=10^[(1/2)^(n-1)]