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Home/ Questions/Q 1741
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Nimit Singh
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Nimit Singh
Asked: December 27, 20202020-12-27T04:04:11+00:00 2020-12-27T04:04:11+00:00In: Class 10 Maths

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.

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NCERT Solutions for Class 10 Maths Chapter 5
Important NCERT Questions
Arithmetic Progression
NCERT Books for Session 2022-2023
CBSE Board and UP Board Others state Board
EXERCISE 5.4
Page No:115
Questions No:4

2020-2021arithmetic progressioncbsechapter 5class10mathematicsncert
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    1. Nairiti
      2021-07-29T05:50:08+00:00Added an answer on July 29, 2021 at 5:50 am

      Get Hindi Medium and English Medium NCERT Solution for Class 10 Maths to download.
      Please follow the link to visit website for first and second term exams solutions.
      https://www.tiwariacademy.com/ncert-solutions/class-10/maths/chapter-5/

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      jaanvi roy
      2023-01-31T10:34:38+00:00Added an answer on January 31, 2023 at 10:34 am

      Here, a = 1 and d = 1.
      Sum to n terms of an AP is given by
      S_n = n/2[ 2a + (n -1)d]
      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. Therefore
      Sx-₁ = S₄₉ – Sx
      ⇒ (x -1/2)[2a + (x – 1 – 1)d]
      ⇒ 49/2[2a + (49 – 1)d] – x/2[2a + (x -1)d]
      ⇒ x -1/2[2(1) + (x -2)(1)]
      ⇒ 49/2[2(1) + 48(1)] – x/2[(1) + (x – 1)(1)]
      ⇒ (x – 1)[x] = 49[50] – x[x + 1]
      ⇒ x² – x = 2450 – x² – x
      ⇒ 2x² = 2450 x² = 1225 ⇒ x = 35
      Hence, the value of x is 35.

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