Question

已知等差数列{an}的前n项和伟sn,公差d≠0,且s3+s5=50,a1,a4,a13城等比数列。求数

Answer 1

已知等差数列{an}的前n项和伟sn,公差d≠0,且s3+s5=50,a1,a4,a13城等比数列。
求数{an}通项。
Sn=a1*n+[n(n-1)d]/2
S3=3a1+[3(3-1)d]/2 =3a1+3d
S5=5a1+[5(5-1)d]/2 =5a1+10d
因为 s3+s5=50
所以 3a1+3d + 5a1+10d=50
即： 8a1+13d=50
a1a13=a4a4
a1(a1+12d)=(a1+3d)^2
12a1d=9d^2
a1=3/2d
25d=50
d=2
a1=3
an=3+2(n-1)=2n+1

Answer 2

s3+s5=3a1+3d+5a1+10d=8a1+13d=50
a1a13=a4^2
a1(a1+12d)=(a1+3d)^2
2a1d=3d^2
a1=3d/2
8a1+13d=50
d=2
a1=3
an=a1+(n-1)d=3+2(n-1)=2n+1