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)

400 = 41N - N2

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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