等差数列{an}中,a1=4,公差d不等于0,若a1,a7,a10成等比数列,求以a1,a7,a10为前三项的等比数列的前n项和

Question

等差数列{an}中,a1=4,公差d不等于0,若a1,a7,a10成等比数列,求以a1,a7,a10为前三项的等比数列的前n项和

Answer 1

a7=a1+6d
a10=a1+9d
(a7)^2=a1*a10
(4+6d)^2=4*(4+9d)
解得d=-1/3或者d=0(舍去)
所以等比数列
b1=4 b2=2 b3=1
首项为4 公比为1/2
Sn=4*[1-(1/2)^n]/(1-1/2)
Sn=8*[1-(1/2)^n]