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標題:
Maths about A.S.&G.S.
發問:
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... 顯示更多 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.
最佳解答:
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
Maths about A.S.&G.S.
發問:
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... 顯示更多 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.
最佳解答:
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
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