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

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