Q. 194.4( 249 Votes )
200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row,18 in the row next to it and so on (see Fig. 5.5). In how may rows are the 200 logs placedand how many logs are in the top row?

Answer :
As, the rows are going up, the no of logs are decreasing,
20, 19, 18, ...,
it's an AP
Suppose 200 logs are arranged in 'n' rows, then
We have;
First term, a = 20,
Common difference, d = - 1 and
Sum of n terms, Sn = No of logs = 200
We know;
200
400= (40 - N +1)
N2 -41N +400 =0
(N -16)(N –25)
Thus, n = 16 and n = 25
If number of rows is 25 then;
a25 = 20 + 24 x (- 1)
= 20 – 24 = - 4
Since; negative value for number of logs is not possible hence; number of rows = 16
a16 = 20 + 15 x (- 1)
= 20 – 15 = 5
Thus, number of rows = 16 and number of logs in top rows = 5
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PREVIOUSA spiral is made up of successive semicircles, with centres alternately at A and B,starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown inFig. 5.4. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take
[Hint : Length of successive semicircles is with centres at A, B, A, B, . . .,respectively.]NEXTIn a potato race, a bucket is placed at the starting point, which is 5 m from the first potato,and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in theline (see Fig. 5.6).
A competitor starts from the bucket, picks up the nearest potato, runs back with it, deposit in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint : To pick up the first potato and the second potato, the total distance (in metres)run by a competitor is
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