Question

若Sn是公差不为0的等差数列｛an｝的前n项和,且S1,S2,S4成等比数列：

Answer 1

设公差为d

由题意,

S1=a1

S2=2a1+d

S4=4a1+6d

a1*(4a1+6d)=(2a1+d)^2

d^2-2a1*d=0

d(d-2a1)=0

d不等于0

所以d=2a1

(1)

公比q=S2/S1=(2a1+d)/a1=(4a1)/a1=4

(2)

S2=a1+a2=2a1+d=4a1=4

a1=1

d=2a1=2

an=a1+(n-1)d=1+(n-1)*2=2n-1