Question

设等比数列an的前n项和为sn,若s3=2,s6=18,则s10/s5=?

Answer 1

S6/S3=A1(1+q+q^2+q^3+...+q^5)/A1(1+q+q^2)=(1+q^3)(1+q+q^2)/(1+q+q^2)=1+q^3=9
所以q=2
同理S10/S5=1+q^5=1+2^5=33

Answer 2

Sn=a1(q^n-1)/(q-1)
S6/S3=[a1(q^6-1)/(q-1)]÷[a1(q^3-1)/(q-1)]=(q^6-1)/(q^3-1)
=(q^3+1)(q^3-1)/(q^3-1)=q^3+1=18/2=9
得q=2
S10/S5=(q^10-1)/(q^5-1)=(q^5+1)(q^5-1)/(q^5-1)=q^5+1
=2^5+1=32+1=33