记数列{an}的前n项和为Sn,若3a(n+1)=3an+2(n属于N*),a1+a3+a5+……a99=99,求S100

问题描述:

记数列{an}的前n项和为Sn,若3a(n+1)=3an+2(n属于N*),a1+a3+a5+……a99=99,求S100
()里为角标

3a(n+1)=3an+23a(n+1)-3an=2a(n+1)-an=2/3数列{an}为等差数列,公差d=2/3a1+a3+a5+...+a99=99a2=a1+2/3 a4=a3+2/3...a100=a99+2/3a2+a4+...+a100=99+50*(2/3)=99+100/3=397/3S100=(a1+a3+...+a99)+(a2+a4+...+a100)=9...