数列an是等比数列,sn是前n项和 ,s4s10s7是等差数列,求a1a7a4也是等差数列
问题描述：
数列an是等比数列,sn是前n项和 ,s4s10s7是等差数列,求a1a7a4也是等差数列
答
S4=a1(1-q^4)/(1-q)
S7=a1(1-q^7)/(1-q)
S10=a1(1-q^10)/(1-q)
2S10=S4+S7
2(1-q^10)=(1-q^4)+(1-q^7)
2q^10=q^4+q^7
2q^6=1+q^3
2a1q^6=a1+a1q^3
2a7=a1+a4
a7-a1=a4-a7
a1a7a4等差数列