(Q36).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. In how many rows are the 200 logs placed and how many logs are in the top row?

Given: Total logs = 200

Number of logs stacked in the first row = 20

Number of logs stacked in the second row = 19

Number of logs stacked in the third row = 18

The number series is 20, 19, 18,….. is an A.P where a = and

d = a2 – a1 = – = -

Also, Sn =

∴ Sn =
n
2
 [2a + (n-1)d]
=
n
2
 [2× + (n-1)×(-)]
=
n
2
 [ - n + 1]
=
n
2
 [ - n]

= n – n2

⇒ n2 – n + = 0

⇒ n2 – n – n + = 0

⇒ (n – ) – (n – ) = 0

⇒ (n – ) (n – ) = 0

⇒ n = (or)

There can’t be rows as we are starting with 20 logs in the first row.

∴ Number of rows must be .

∴ n =