標題:
Let S(n)=n^2+3n be the sum of the first n terms of a sequen
發問:
Let S(n)=n^2+3n be the sum of the first n terms of a sequen a) (i)Find the sum of T(1)+T(2)+...+T(10). (ii)Find the sum of T(1)+T(2)+....+T(9). (iii)Hence find T(10). b)Find T(n). c)What kind of sequence is T(1),T(2),T(3),....?
最佳解答:
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i)Find the sum of T(1)+T(2)+...+T(10). S(10)=10^2+3(10)=130 (ii)Find the sum of T(1)+T(2)+....+T(9). S(9)=9^2+3(9)=108 (iii)Hence find T(10). T(10)=S(10)-S(9)=22 b)Find T(n). T(1)=S(1)=4 T(2)=S(2)-S(1)=10-4=6 T(3)=S(3)-S(2)=18-10=8 T(4)=S(4)-S(3)=28-18=10 T(5)=S(5)-S(4)=40-28=12 and so on T(n)=2(n+1) S(n)=[4+2(1+n)]n/2=(2+1+n)n=n^2-3n c)What kind of sequence is T(1),T(2),T(3),....? AP
其他解答:
a(i)T(1)+T(2)+...+T(10) =S(10) =10^2+3x10 =130 (ii)T(1)+T(2)+....+T(9) =S(9) =9^2+3x9 =108 (iii)T(10) =S(10)-S(9) =22 bT(n)=S(n)-S(n-1) =n^2+3n-(n-1)^2-3(n-1) =2n+2 c.arithmetic sequence
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