Question

等差数列中,a16 a17 a18=a9=-36,前n项和为Sn.求Sn最小值,求Sn最小值时n的值

Answer 1

a16+a17+a18=a9=-36

3a17=a9=-36

3(a1+16d)=a1+8d=-36

a1=-60,d=3

Sn=na1+n(n-1)d/2=3/2(n^2-41n)=3/2(n-41/2)^2-5043/8

S20=3/2(20^2-41*20)=-630

S21=3/2(21^2-41*21)=-630

因此,当n=20,或n=21时,Sn最小值=-630