已知公差数列大于零的等差数列{an}的前n项和为Sn,且满足a3*a4=117,a2+a5=22 (1)求数列{an}的通项公式an;(2)若数列{bn}是等差数列,且bn=Sn/(n+c),求非零常数c

问题描述:

已知公差数列大于零的等差数列{an}的前n项和为Sn,且满足a3*a4=117,a2+a5=22 (1)求数列{an}的通项公式an
;(2)若数列{bn}是等差数列,且bn=Sn/(n+c),求非零常数c

(1)a3*a4=117a3+a4=a2+a5=22故a3、a4是一元二次方程x^2-22x+117=0的两个根.也即(x-9)(x-13)=0解得x=9或x=13因公差大于零,故a4>a3,则a3=9,a4=13,d=a4-a3=4,an=a3+(n-3)d=9+4(n-3)=4n-3 (2)Sn应该是{an}的前n项和...