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360 bricks are stated in the …

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360 bricks are stated in the following manner 13 bricks in the bottom row 29 weeks in the next 2 and 28 weeks in the role next to it and so on in how many rows 360 bricks are placed and how many bricks are there in the top row
  • 1 answers

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+(n1)(1)]=360        {Sn=n2(2a+(n1)d)}

720=n(60n+1)

720 = 60n - n2+n

n261n+720=0

n216n45n+720=0 [by factorisation]

n(n16)45(n16)=0

(n16)(n45)=0

(n16)=0 or (n45)=0

n=16 or n=45

Hence, number of rows is either 45 or 16.

When, n=16,

a16=30+(161)(1)     {an=a+(n1)d}

=3015=15

When, n=45

a45=30+(451)(1)        {an=a+(n1)d}

=3044=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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