已知等差数列{An}中,d>0,钱n项和为Sn,且满足a2*a3=45,a1+a4=14.通过公式Bn=Sn/(n+c)构造一个数列{Bn}

问题描述:

已知等差数列{An}中,d>0,钱n项和为Sn,且满足a2*a3=45,a1+a4=14.通过公式Bn=Sn/(n+c)构造一个数列{Bn}
若其也是等差数列,求非零常数c

a2*a3=(a1+d)(a1+2d)=45 (1)a1+a4=2a1+3d=14 (2)(2) 得出a1=7-3/2d (3)代入(1)解得d=4(>0)代入(2)解得a1=1Sn=(2a1+(n-1)d)*n/2=(2n-1)*n (4)S1=1,S2=6,S3=15Bn为等差数列,则必有2B[n]=B[n-1]+B[n+1]B1=1/(1+c),B...