在数列an中a3等于2a7等于1若（an＋1）分之一为等差数列则a19等于多少

Question

在数列an中a3等于2 a7等于1 若（an＋1）分之一为等差数列 则a19等于多少

Answer 1

let
bn = 1/(an+1)
bn = b1+(n-1)d
b7 -b3 = 4d
1/(a7+1) - 1/(a3+1) = 4d
1/2 -1/3 =4d
d = 1/24
b19 = b7 +12d
=1/2 +1/2
=1
b19 = 1/(a19+1)
a19+1 = 1
a19=0