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 the fig. given below). In how many rows are the 200 logs placed and how many logs are In the top row?

Answer 1

20, 19, 18, ….. 

a = 20, d = 19 – 20 = -1 

S_n = 200, n =?, a_n =?

∴ 400 = n(41 – n) 

400 = 4n – n² 

∴ n² – 41n + 400 = 0 

n² – 25n – 16n + 400 = 0

n(n – 25) – 16(n – 25) = 0 

(n – 25) (n – 16) = 0

if n – 16 = 0 then, n = 16 

∴ a_n = a + (n – 1)d 

a₁₆ = 20 + (16 – 1) (-1) 

= 20 + 15(-1) = 20 – 15 

∴ a₁₆ = 5 

∴ 200 logs are placed In 16 rows and there are 5 logs in the top row.