Question

360 bricks are stacked in the following manner ,30 bricks in the bottom row ,29 bricks in the next row , 28 bricks in the row next to it and so on. In how many rows 360 bricks are placed and how many bricks are there in the top row ?

Answer 1

Here the number of rows is decreasing by 1 from 30 to some number of rows .

Let number of rows = n

Given Sn = 360

sequence is in AP = 30, 29, 28, 27,.........,

here a = 30 and d = -1.

we know that  Sn = n/2 (2a + (n - 1)d )

⇒ 360 = n/2 (60 + (n - 1) -1)

⇒ 720 = n (60 - n + 1)

⇒ -n2 + 61n = 720

⇒ n2 - 61n + 720 = 0

⇒ n2 - 16n - 45n + 720 = 0

⇒ n (n - 16) - 45 (n -16) = 0

⇒ (n -16) (n - 45) = 0

∴n = 16 or n = 45.

but n can 't be 45. (after 30 rows everything is negative)

∴the number of rows is 16

Number of bricks in top row  = an = a + (n – 1)d.

an = 30 + (15)-1

an = 30 - 15.

an = 15 .

Answer 2

here is your answer
hope it helps