Maths Question 非常急

2007-11-11 6:01 am

1.Find the general term for each sequence.
T[2]=5,T[7]=160

2.Find the general term for each sequence.[leave your answers in surd form if necessary]
T[2]=-9,T[6]=-729/256

3.A ball is dropped vertically from the top of a building.Each time it reaches the ground,it rebounds to a height which is 3/5 of its previous height.If the ball reaches a height of 1.62m after the fourth rebound,find the height of the building.

回答 (1)

ゾルディック

2007-11-11 7:04 am

✔ 最佳答案

1.Let A and R be the first term and the cmmn rati respectively
T[2]=AR=5..........(1)
T[7]=AR^6=160....(2)
(2)/(1):
R^5=32
R=2
Sub into (1)
2A=5
A=5/2
T(n)=AR^(n-1)
T(n)=(5/2)．2^(n-1)
Ans:T(n)=5．2^(n-2)

2.Let A and R be the first term and the cmmn rati respectively
T[2]=AR=-9..........(1)
T[6]=AR^5=-729/256....(2)
(2)/(1):
R^4=81/256
R=3/4 or-3/4
Sub into (1)
(3/4)A=-9
A=-12
T(n)=AR^(n-1)
T(n)=(-12)．(3/4)^(n-1)
Sub into (1)
(-3/4)A=-9
A=12
T(n)=AR^(n-1)
T(n)=(12)．(3/4)^(n-1)
Ans:T(n)=(12)．(3/4)^(n-1) or T(n)=(-12)．(3/4)^(n-1)

3.A be the height of the building and R be the rebund
T[2]=AR
T[3]=AR^2
T[4]=AR^3
T[5]=AR^4=1.62
A(3/5)^4=1.62
A=1.62/0.6=12.5
Ans:The height f the building is 12.6m.

參考: Certificate Mathematics in Action 5A(Ex.14D 17,22,27)

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