Math, asked by dineshpayasidgs, 1 year ago

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

Answers

Answered by Anonymous

Answer-

Given that the logs are placed is a order of 20, 19, 18 and so on.

This forms an A.P. where a = 20 and d = (-1)

Also, the total number of logs = 200

Now,

$Sn = 200$

$Sn = \frac{n}{2} [2a + (n - 1)d]$

$200 = \frac{n}{2}[ 2 \times 20 + (n - 1) - 1]$

$200 = (40 - n - 1)$

$400 = n(41 - n)$

$400 = 41n - {n}^{2}$

${n}^{2} - 41n + 400 = 0$

$= > n = 16 \: and \: n = 25$

Substituting value of n to be 16, we get:

$an = a + (n - 1)d$

$a16 = 20 + (16 - 1) - 1$

$a16 = 20 - 15$

$a16 = 5 \: (possible)$

Substituting value of a to be 25, we get:

$a25 = 20 + (25 - 1) - 1$

$a25 = - 4 \: (not \: possible)$

Hence, the total number of row is 16 and logs in top row is 5.

Answered by XxMissPaglixX

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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).

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.

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