Question

数列{an}中，a3=2,a7=1,且数列{1/（an+1)}是等差数列，则an=？

(请给出解释，谢谢！）

Answer 1

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)

Answer 2

{1/（an+1)}是等差数列
d=(1/a7-1/a3)/4=(1-1/2)/4=1/8
1/a1=1/a3-2d=1/2-2*1/8=1/4
1/an=1/a1+(n-1)d=1/4+(n-1)/8=(n+1)/8
an=8/(n+1)

Answer 3

额