等差数列an的各项均为正数,a1=1前n项和为sn数列bn为等比数列b1=2且b2s2=16,b3s3=72.求an bn通项

等差数列an的各项均为正数,a1=1前n项和为sn数列bn为等比数列b1=2且b2s2=16,b3s3=72.求an bn通项
等差数列an的各项均为正数,a1=1前n项和为sn数列bn为等比数列b1=2且b2s2=16,b3s3=72.求an bn通项

等差数列an的各项均为正数,a1=1前n项和为sn数列bn为等比数列b1=2且b2s2=16,b3s3=72.求an bn通项
设{an}公差为d,{bn}公比为q.
等差数列{an}各项均为正,则公差d≥0
b2S2=16 b3S3=72
(b1q)×(2a1+d)=16
(b1q²)×(3a1+3d)=72
a1=1 b1=2代入,整理,得
q(d+2)=8 (1)
q²(d+1)=12 (2)
(1)²/(2)
(d+2)²/(d+1)=64/12
整理,得
3d²-4d-4=0
(3d+2)(d-2)=0
d=-2/3(