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

Philoid · Accepted Answer

We have; a = 20, d = - 1 and S_n = 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