求数列5,8,11,16,17,24,23,...前50项的和

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/26 12:04:14
求数列5,8,11,16,17,24,23,...前50项的和求数列5,8,11,16,17,24,23,...前50项的和求数列5,8,11,16,17,24,23,...前50项的和5,8,11,

求数列5,8,11,16,17,24,23,...前50项的和
求数列5,8,11,16,17,24,23,...前50项的和

求数列5,8,11,16,17,24,23,...前50项的和
5,8,11,16,17,24,23
设{An}=5,11,17,23,...,5+6(n-1)
{Bn}=8,16,24,...,8*n

原数列和Sn=S(A25)+S(B25)=[25*5+25*(25-1)*6/2]+8(1+2+3+...+25)=4525
++++++++++++++++
设k=n/2
Sn=k*5+k(k+1)*6/2+8*k(k+1)/2 =7k^2+6k=(7n^2+12n)/4
n为偶数,n>0