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. And find this value of x.[Hint : Sx – 1 = S49 – Sx]
Answers
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:
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.