等差数列{an}的各项均为正数,a1=3,其前项和为Sn,{bn}为等比数列,b1=1且b2S2=16,b3S3=60.求{an}与{bn}

等差数列{an}的各项均为正数,a1=3,其前项和为Sn,{bn}为等比数列,b1=1且b2S2=16,b3S3=60.求{an}与{bn}
等差数列{an}的各项均为正数,a1=3,其前项和为Sn,{bn}为等比数列,b1=1且b2S2=16,b3S3=60.求{an}与{bn}

等差数列{an}的各项均为正数,a1=3,其前项和为Sn,{bn}为等比数列,b1=1且b2S2=16,b3S3=60.求{an}与{bn}
设{an}公差为d,数列各项均为正,则d≥0.设{bn}公比为q.
b2S2=q(2a1+d)=q(d+6)=16
b3S3=q²(3a1+3d)=q²(3d+9)=60
q(d+6)=16 (1)
q²(d+3)=20 (2)
(2)/(1)²
(d+3)/(d+6)²=20/16²
整理,得
5d²-4d-12=0
(d-2)(5d+6)=0
d=2或d=-6/5(