等差数列An,S4=44,S1=35,求An及Sn

问题描述:

等差数列An,S4=44,S1=35,求An及Sn

S1=A1=35
S4=A1+A2+A3+A4
=A1+A1+d+A1+2d+A1+3d
=4A1+6d
=44
因为d=-16
所以An=35+(n-1)*(-16)=51-16n
Sn=35n+[n(n-1)/2]*(-16)=35n-8n(n-1)

设首项和公差分别为A1,d,则
S1=A1=35
S4=A1+A2+A3+A4
=A1+A1+d+A1+2d+A1+3d
=4A1+6d
=44
从d=-16
故An=35+(n-1)*(-16)=51-16n
Sn=35n+[n(n-1)/2]*(-16)=35n-8n(n-1)