Question

在等差数列{an}中,a4=10,a3,a6,a10成等比数列求数列an前10项和S10

Answer 1

设A3 = x , 公差是d

a4= x + d = 10 ; d = 10 - x

a3*a10 = a6^2 ; x(x+6d) = (x+3d)^2 ; x(x+6(10-x)) = (x+3(10-x))^2

得 x = 10 或 x = 9

当x = 9 时 d =10 -9 =1

a3 = 9 a4 = 10 a6 = 12 a10 = 16 满足 9*16 = 12^2

a1 = a3 -2d=9-2=7 a10 =a3+7d = 9+7=16

则 S10 = (a1+a10)*10/2=(7+16)*10/2 = 115

党x = 10 时 d = 10 -10 =0

a3 = 10 -0 =10

则An = 10

S10 = 10*10 =100