Question

等比数列的前n和为Sn,已知S1,S3,S2成等比数列,求 1,公比q.

Answer 1

(1)S3-S1=S2-S3a1+a2+a3-a1=a1+a2-a1-a2-a3 a2+2a3=0 a2+2a2q=0 q=-1/2(2)a1-a3=3 a1-a1/4=3 a1=4Sn=a1(1-q^n)/(1-q)=4[1-(-1/2)^n]/(3/2)=8[1-(-1/2)^n]/3