Question

等差数列{an}的公差为d〈0,且a3+a9=50,a5a7=-616,求此数列前多少个项和最大,并求最大值

Answer 1

a3+a9=50=a1+2d+a1+8d

25=a1+5d

a1=25-5d

a5a7=-616=(a1+4d)(a1+6d)

-616=(25-5d+4d)(25-5d+6d)

d=-√1241

a1=25+5√1241

an=a1-(n-1)√1241=0时,n=6时,Sn最大.

Sn=6a1+15d

=6(25+5√1241)-15√1241

=150+15√1241