求数列5,8,11,16,17,24,23,...前50项的和

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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

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
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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