for an arithmetic sequence with general term T(n),the 5th term is four times the first term,and the 6th term is less than two times the 3rd term by 1.find
(a)T(n)
(b)the value of m if T(m)-T(25)=81
maths question
2012-09-15 2:35 am
回答 (1)
2012-09-15 2:58 am
✔ 最佳答案
Let T(n)=a+(n-1)dT(5)=4T(1)
a+4d=4a
3a=4d ...........(i)
T(6)=2T(3)-1
a+5d=2(a+2d)-1
a=d+1 ..........(ii)
From (i), (ii), we get a=4 and d=3, so
T(n)=4+3(n-1)=1+3n (Ans)
T(m)-T(25)=81
1+3m-1-75=81
3m=156
m=52 (Ans)
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