已知递增数列{an}满足a1=1,(2an+1)=an+(an+2),且a1,a2,a4成等比数列.求an

已知递增数列{an}满足a1=1,(2an+1)=an+(an+2),且a1,a2,a4成等比数列.求an
已知递增数列{an}满足a1=1,(2an+1)=an+(an+2),且a1,a2,a4成等比数列.求an

已知递增数列{an}满足a1=1,(2an+1)=an+(an+2),且a1,a2,a4成等比数列.求an
(2an+1)=an+(an+2)可知an是等差数列
a1=1
设an=(n-1)d+1
a1=1
a2=d+1
a4=3d+1
因为a1,a2,a4等比
所以(d+1)^2=(3d+1)*1
d=0 or d=1
因为an递增,所以d>0
d=1
所以an=n