Question

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Answer 1

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Answer 2

Observed that the numbers of logs in rows are in an A.P.

20, 19, 18…..........

For this A.P.,

a = 20

d = a2 − a1 = 19 − 20 = −1

Let a total of 200 logs be placed in n rows.

Sn = 200

Sn = (n / 2)[ 2a + (n – 1)d]

⇒ 200 = (n / 2)[ 40 + (n – 1)(-1)]

⇒ 400 = n (40 − n + 1)

⇒ 400 = n (41 − n)

⇒ 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) = 0 or n − 25 = 0

n = 16 or n = 25

n = 25 reject it.Because of number of rows cannot be more than 20.

∴ n = 16.

an = a + (n − 1)d

a16 = 20 + (16 − 1) (−1)

a16 = 20 − 15

a16 = 5.

Thus there are 16 rows and 5 logs in the top row.



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