设等差数列{an}的前n项和为Sn,a1=3/2,且S1,S2,S4成等差数列,求Sn

问题描述:

设等差数列{an}的前n项和为Sn,a1=3/2,且S1,S2,S4成等差数列,求Sn

设公差为d
则S1=3/2,S2=3/2+3/2+d=3+d,S4=6+6d
又S1,S2,S4成等差数列,所以2*S2=S1+S4
解得d=-3/8
所以Sn=a1*n+(n-1)*n*d/2=3n(9-n)/16