Question

一道高一数学必修5的题已知等差数列{an}的公差是正数,且a3a7=-12,a4+a6=-4,求{an}的通项公式.

Answer 1

2a5=a4+a6=-4

a5=-2

a3a7=-12

(a5-2d)(a5+2d)=-12

a5^2-4d^2=-12

4d^2=16

d^2=4

d=2或d=-2(舍去)

a1=a5-4d=-2-4*2=-10

an=a1+(n-1)d

=-10+(n-1)*2

=2n-12