Question

等比数列{a n}的前n项和为sn,已知S1,S2,S3成等差数列(1)求{a n}的公比q（2）求a1-a3=3,求S

Answer 1

S1=a1

S2=a1(1+q)

S3=a1(1+q+q^2)

S1,S3,S2成等差数列

即

s3-s1=s2-s3

1+q+q^2-1=1+q-(1+q+q^2)

q^2+q=-q^2

q=0或-1/2

如果a1-a3=3

a1不等于a3

q不等于0,即q=-1/2

a1(1-1/4)=3

a1=4

所以Sn=4*(1-(-1/2)^n)/(3/2)=8*(1-(-1/2)^n)/3