Question

已知等差数列{an}的公差d大于0,且a2,a5是方程x^2-12x+27=0的两根,求数列{an}的前n项和Sn

Answer 1

等差数列{a[n]},公差大于零,a2、a5是方程x^2-12x+27=0的两根

a2=3=a1+d,a5=9=a1+4d

解得：a1=1,d=2

an=1+2(n-1)=2n-1

sn=na1+n(n-1)d/2=n+n^2-n=n^2