Home
Class 10
MATHS
The houses of a row are numbered consecu...

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: `S_[x-1]=S_[49]-S_x`)

Promotional Banner

Topper's Solved these Questions

  • AREAS RELATED TO CIRCLES

    RD SHARMA|Exercise All Questions|251 Videos

  • CIRCLES

    RD SHARMA|Exercise All Questions|131 Videos

Similar Questions

Explore conceptually related problems

The houses of a row are numbered 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

Find the sum of face values of all the 8's in the number 87388243.

The houses on one side of a road are numbered using consecutive even numbers .The sum of the numbers of all the houses in that row is 170. If there are at least 6 houses in that row and a is the number of the sixth house then

Find the sum of face values of all the 8's in the number 8738823.

In the number 98769246, find the sum of plae values of both the 9's .

(B) The number of integral pair(s) (x,y) whose sum is equal to their product is

In the number 98739246, find the sum of place values of both the 9's.

RD SHARMA-ARITHMETIC PROGRESSIONS-All Questions
  1. The digits of a positive integer, having three digits, are in A.P. and...

    Text Solution

    |

  2. A man repays a loan of R s .3250 by paying R s .20 in the first month ...

    Text Solution

    |

  3. The houses of a row are numbered consecutively from 1 to 49. Show that...

    Text Solution

    |

  4. A ladder has rungs 25 cm apart, (see Figure). The rungs decrease un...

    Text Solution

    |

  5. A small terrace at a football ground comprises of 15 steps each of ...

    Text Solution

    |

  6. A spiral is made up of successive semicircles, with centres alterna...

    Text Solution

    |

  7. In a potato race, a bucket is placed at the starting point, which is ...

    Text Solution

    |

  8. Find the sum of the following arithmetic progressions: 50 ,\ 46 ,\ ...

    Text Solution

    |

  9. Find the sum of the following arithmetic progressions: 41 ,\ 36 ,\ ...

    Text Solution

    |

  10. Find the sum of the following arithmetic progressions: (x-y)/(x+y)\...

    Text Solution

    |

  11. Find the sum to n term of the A.P. 5,\ 2,\ -1,\ -4,\ -7,\ dot,

    Text Solution

    |

  12. Find the sum of n terms of an A.P. whose n t h terms is given...

    Text Solution

    |

  13. If the sum of a certain number of terms of the A.P. 25, 22, 19.... ...

    Text Solution

    |

  14. How many terms of the sequence 18 ,\ 16 ,\ 14 ,\ dot should be t...

    Text Solution

    |

  15. How many terms are there in the A.P. whose first and fifth terms are ...

    Text Solution

    |

  16. How many terms of the A.P. 9,\ 17 ,\ 25 ,\ dot must be taken so ...

    Text Solution

    |

  17. How many terms of the A.P. 63, 60, 57, .... must be taken so that t...

    Text Solution

    |

  18. The first and the last terms of an AP are 17 and 350 respectively. ...

    Text Solution

    |

  19. The third term of an A.P. is 7 and the seventh term exceeds three time...

    Text Solution

    |

  20. The first term of an A.P.is 2 and the last term is 50. the sum of all ...

    Text Solution

    |