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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.

Q : 4    The houses of a row are numbered consecutively from to . Show that there is a value of   such that the sum of the numbers of the houses preceding the house numbered is equal to the  sum of the numbers of the houses following it. Find this value of .                                                              [Hint :

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It is given that the sum of the numbers of the houses preceding the house numbered is equal to the  sum of the numbers of the houses following it
And 1,2,3,.....,49 form an AP with a = 1 and d = 1
Now, we know that

Suppose their exist an n term such that ( n < 49)
Now, according to given conditions
Sum of first n - 1 terms of AP = Sum of terms following the nth term
Sum of first n - 1 terms of AP = Sum of whole AP - Sum of first m terms of AP
i.e.

Given House number are not  negative so we reject n = -35

Therefore, sum of no of houses preceding the house no 35 is equal to the sum of no of houses following the house no 35

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