The houses in a row are numbered consecutively from to

MATHEMATICS · Subjective · CBSE · Mathematics · Arithmetic Progressions · Arithmetic Progressions

Problem

The houses in a row are numbered consecutively from 11 to 4949. Show that there is a value of xx such that the sum of the numbers of the houses preceding house xx equals the sum of the numbers of the houses following it. Find xx. Hint: Sx−1=S49−SxS_{x-1}=S_{49}-S_x.

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