Question

已知等差数列{an}的公差为正数,且a3*a7=-12,a4*a6=0,则s20=?

Answer 1

a3*a7=-12 [a5-2d]*[a5+2d]=a5^2-4d^2=-12

a4*a6=0 [a5-d]*[a5+d]=a5^2-d^2=0 d=2 a5=-2

a1=a5-4d=-10

a20=a1+19d=-10+38=28

s20=(a1+a20)*20/2=180