Question

200 logs are stacked in the following manner :20 logs in bottom row ,19 in next row , 18 in the row next to it and 50 on. in how many rows 200 logs are placed and how many logs are in the top row

Answer 1

hope this answer helps you

Answer 2

SOLUTION Let the required number of rows be n. Then,

20+ 19 + 18+ .. to n terms = 200.

This is an arithmetic series in which

a = 20, d = (19-20) = -1 and S, = 200.

We know that S 12a + (n-1)d).

2

12 20 + (n − 1)(-1)) = 200

(41 - n) = 400 = n2-41n + 400 = 0

712-25n -16n + 400 = 0 => n(n-25) - 16(1-25) = 0

(n1 - 25) (11-16) = 0 = 11-25 = 0 or 11-16 = 0

n = 25 or n = 16.

Now, T = (a +24d) = 20 + 24 (-1) = -4.

This is meaningless as the number of logs cannot be negative

So, we reject the value n = 25.

11 = 16. Thus, there are 16 rows in the whole stack

Now, T = (a +150) = 20 + 15 X (-1) = 20 - 15 = 5.

Hence, there are 5 logs in the top row.