Maths about A.S.&G.S.

2011-09-25 5:47 am

37. A snake starts moving at a speed of 2m per second towards a target which is 5.8m away. In each second, the snake only moves two- thirds of the distance it travelled in the previous second. (a) Find the total distance that the snake has moved in the first 5 seconds. (b) Find the total distance that the snake can travel.

回答 (1)

賣女孩的火柴

2011-09-25 6:23 am

✔ 最佳答案

37.
(a)
T(n): The distance in m that the snake moves in the nth second.

T(1) = 2
T(2) = 2 ´ (2/3)
T(3) = 2 ´ (2/3)^2
......
T(n) = 2 ´ (2/3)^(n - 1)

T(1), T(2), T(3), ...... ,T(n), ..... form a geometric sequence, where
the first term, T(1) = a = 2
and the common ratio, r = 2/3

S(5)
= a(1 - r^n)/(1 - r)
= 2[1 - (2/3)^5] / [1 - (2/3)]
= 2[1 - (32/243)] / (1/3)
= (422/243) / (1/3)
= 422/81

The total distance that the snake has moved in the 1st 5 seconds
= 422/81 m
≈ 5.21 m

(b)
S(∞)
= a/(1 - r)
= 2/[1 - (2/3)]
= 6

The total distance that the snake can travel
= 6 m

參考: 賣女孩的火柴

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