令bn=1/(an+1),则bn是等差数列,设公差为d
b3=b1+2d=1/3,b7=b1+6d=1/2
故d=1/24,b1=1/4
bn=1/24+(n-1)/4=(n+5)/24
即1/(an+1)=(n+5)/24
an=(19-n)/(n+5)