Question

an是等差数列,bn 是等比数列,a1+b1=3,a2+b2=7,a3+b3=15,a4+b4=35,求an+bn=?

Answer 1

a1+b1=3 (1)

a2+b2=7 (2)

a3+b3=15 (3)

a4+b4=35 (4)

(1)+(3)-(2)*2 得到 b1*(q²-2q+1)=4 (5)

(2)+(4)-(3)*2 得到 b2*(q²-2q+1)=12 (6)

(6)/(5)有：q=3,代入（5）有,b1=1,代入(1)有

a1=2,

b2=3,代入（2）有a2=4

从而an=2n,bn=3^(n-1)

an+bn=2n+3^(n-1)