已知Sn是等比数列an的前n项,如果a2,a8,a5成等差数列,那么S3,S9,S6成等差数列吗?请说明理由_数学解答

已知Sn是等比数列an的前n项,如果a2,a8,a5成等差数列,那么S3,S9,S6成等差数列吗?请说明理由

人气：444 ℃　时间：2019-11-06 12:02:16

解答

2a8=a2+a5
2a1q^7=a1(q+q^4
2q^6=1+q^3,a^3=1,or q^3=-1/2
S3+S6=a1[q^3-1+q^6-1]/(q-1)=a1(q^3+q^6-2)/(q-1)=0 or -2.25a1/(q-1)
2S9=2a1(q^9-1)/(q-1)= 0 or -2.25a1/(q-1)
所以无论q^3=1 or q^3=-1/2,S3,S9.S6都成等差数列.