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?

Question

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?
A diagram labeled Fig. 5.5 illustrates a stack of logs. The logs are arranged in multiple horizontal rows, forming a pyramid-like structure where each successive row from the bottom upwards contains fewer logs. The logs appear cylindrical.

Philoid · Accepted Answer

We have; a = 20, d = - 1 and Sn = 200We know;200 400=  (40 - N +1)N2 -41N +400 =0(N -16)(N &#x2013;25)Thus, n = 16 and n = 25If number of rows is 25 then;a25 = 20 + 24 x (- 1)= 20 &#x2013; 24 = - 4Since; negative value for number of logs is not possible hence; number of rows = 16a16 = 20 + 15 x (- 1)= 20 &#x2013; 15 = 5Thus, number of rows = 16 and number of logs in top rows = 5

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?

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