Question

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The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x. [Hint : Sx-1 = S49 – Sx ]
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Answer 1

Answer:

.

Answer:

Step-by-step explanation:

Let x be the value such that the sum of number of houses preceding the house number x is equal to the sum of numbers of the houses following it.

Thus,

Sum of preceding the numbers of x = sum of following numbers of x

ie Sum of ( 1,2,3,....x-1) = sum of [(x+1), (x+2) ,....48,49]

That is 1 + 2 + 3 + ...... + ( x-1) = ( x+1) + ( x+2) ...... + 49

= (x-1)/2[1+x-1] = (49-x)/2[x+1+49]

= (x-1)x=(49-x)(x+50)

= x²-x=49x+2450-x²-50x

= x²-x =2450-x²-x

= 2x²=2450

= x²=1225

x=√1225

x = 35

Thus, the value of x is 35.

Answer 2

Answer:

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