Question

15. 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 may rows are the 200 logs placed and how many logs are

in the top row?


Standard:- 10

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Answer 1

Hey!!!

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Difficulty Level : NCERT Question :-(

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Given, 200 logs are in total

Can we say Sn = 200

Here the numbers of logs stacked are in AP where

=> a = 20
=> d = - 1
=> Sn = 200

Let's calculate

We know Sn

$= > \frac{n}{2} (2a + (n - 1)d)$

=> 200 = n(40 + (n - 1)(-1))/2

=> 400 = n(40 - n + 1)

=> 400 = 41n - n²

=> n² - 41n + 400 = 0

=> n² - 16n - 25n + 400 = 0

=> n(n - 16) - 25(n - 16) = 0

=> (n - 16)(n - 25) = 0

=> n = 16 or n = 25 <<<<<<< Answer

Now,

Case 1 n = 16

=> l = a + (n - 1)d

=> l = 20 + 15(-1)

=> l = 5

Thus there can be 35 logs in the last row.

Case 2 n = 25

=> l = 20 - 24

=> l = - 4

Since logs cannot be negative Case 1 is true

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Hope this helps ✌️