已知数列[a]是等差数列,其前n项和为Sn,数列[bn]是等比数列,且a1=b1=2,a4+b4=27,S4=b4+10,求a,b的通...已知数列[a]是等差数列,其前n项和为Sn,数列[bn]是等比数列,且a1=b1=2,a4+b4=27,S4=b4+10,求a,b的通项式?

Question

已知数列[a]是等差数列,其前n项和为Sn,数列[bn]是等比数列,且a1=b1=2,a4+b4=27,S4=b4+10,求a,b的通...
已知数列[a]是等差数列,其前n项和为Sn,数列[bn]是等比数列,且a1=b1=2,a4+b4=27,S4=b4+10,求a,b的通项式?

Answer 1

S4=(a1+a4)×4/2=4+2a4
S4=b4+10=27-a4+10=37-a4
4+2a4=37-a4,3a4=33,a4=11
a4=a1+(4-1)d,得d=3,an=2+3(n-1)=3n-1
b4=27-a4=16
b4=b1*q^(n-1)=2*q^3=16,q=2
bn=2*2^(n-1)=2^n