360 bricks are stated in the …
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Sia ? 5 years, 11 months ago
Number of bricks in the bottom row=30. in the next row=29, and so on.
therefore, Number of bricks stacked in each row form a sequence 30, 29, 28, 27,... , which is an AP with first term , a=30 and common difference, d= 29 - 30 = -1.
Suppose number of rows is n, then sum of number of bricks in n rows should be 360
i.e. Sn=360
⇒n2[2×30+(n−1)(−1)]=360 {Sn=n2(2a+(n−1)d)}
⇒720=n(60−n+1)
⇒720 = 60n - n2+n
⇒n2−61n+720=0
⇒n2−16n−45n+720=0 [by factorisation]
⇒n(n−16)−45(n−16)=0
⇒(n−16)(n−45)=0
⇒(n−16)=0 or (n−45)=0
⇒n=16 or n=45
Hence, number of rows is either 45 or 16.
When, n=16,
a16=30+(16−1)(−1) {an=a+(n−1)d}
=30−15=15
When, n=45
a45=30+(45−1)(−1) {an=a+(n−1)d}
=30−44=−14 [∵ The number of logs cannot be neagtive]
Hence, the number of rows is 16 and number of logs in the top row is 15.
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