设等比数列an的前n项和为Sn,若S5=1,S10=33,求an 和sn
问题描述:
设等比数列an的前n项和为Sn,若S5=1,S10=33,求an 和sn
答
设公比为qS10=S5+q^5*S5=(1+q^5)S5=1+q^5=33 1+q^5=33 q=2S5=a1(1-q^5)/(1-q)=a1(2^5-1)=31a1=1 a1=1/31an=a1*q^(n-1)=2^(n-1)/31=2^n/62Sn=a1(1-q^n)/(1-q)=a1(q^n-1)=(2^n-1)/31