Applications of the Summation

Scarbo

2011-10-19 6:26 am

1. A group of students joining agymnastics show are arranged in rows. There are 88 students in the first row,and in each succeeding row, there are 7 students fewer than the preceding row. Supposegirls and boys are arranged in alternate rows with girls in the first row. Findthe number of boys joining the gymnastics show. ANS: 276 2. A ball is released from aheight of 10 m and falls to the ground. the ball rebounds to75% of the height itfalls. Find the total distance travelled before the ball comes to rest. (Hint:You have to consider both the upward and downward distances travelled by theball.) ANS: 70m 3. A train travels 20m in thefirst second after its engine is switched off. In each successive second, thedistance that the train travels is 80% of that in the previous second.a) find, in terms of n,(i) the distance that the traintravels in the nth second,ANS: 20(0.8)^n-1 m(ii) the total distance that thetrain travels in the first nth second,ANS: 100(1-0.8^n) mb) If the driver of the trainswitches off the engine when he discovers an obstacle on the rail 101 m infront of the train, can the train stop successfully without hitting theobstacle? ANS: Yes
How can I get the answer? Thanks!!

回答 (1)

myisland8132

2011-10-19 7:43 am

✔ 最佳答案

1 First term 81, last term is 11

So, the no. of boys

= 81 + 67 + 53 + 39 + 25 + 11

= 276

2 First term 10

Second term = 10 * 75% = 7.5

Third term = 7.5 * 0.75 = 5.625

So, total distance

= 10 + 2(7.5 + 5.625 + ...)

= 10 + 2 * 7.5/(1 - 0.75)

= 10 + 60

= 70 m

3(a)(i) Using formula of gemoetric sequence

The distance that the train travels in the nth second

= 20(0.8)^(n - 1)

(ii) Using the formula of sum of gemoetric sequence

The total distance that the train travels in the first nth second

= 20(1 - 0.8^n)/(1 - 0.8)

= 100(1 - 0.8^n) m

(iii) Let n -> infinity

100(1 - 0.8^n) = 100

So, the train will travel 100 m and it can stop successfully without hitting the obstacle.

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