Question

已知等差数列an的公差是正整数,且a3*a7=-12 a4+a6=-4,则前十项的和sn=

Answer 1

∵an是等差数列

∴a3+a7=a4+a6=-4 ①

又a3×a7=-12 ②

联立①、②解得

a3=-6,a7=2或a3=2,a7=-6

又公差d＞0,

∴a3=-6 ,a7=2

故4d=a7-a3=8

得d=2,a1=a3-2d=-6-2×2=-10

an=a1+(n-1)d=-10+2(n-1)=2n-12

a10=2×10-12=8

S10=10(a1+a10)/2

=5(-10+8)

=-10

答案：-10