设an是正数组成的数列,其前n项和为Sn,并且对于所有的自然数n,an与2的等差中项等于Sn与2的等比中项．

(an +2)/2=√(2Sn)8Sn=(an+2)²n=1时,8S1=8a1=(a1+2)²(a1-2)²=0a1=2n≥2时,8Sn=(an +2)² 8S(n-1)=[a(n-1)+2]²8Sn-8S(n-1)=8an=(an+2)²-[a(n-1)+2]²(an -2)²=[a(n-1)+2]²...