Home
Class 12
MATHS
Show that the sum of all odd integers be...

Show that the sum of all odd integers between and 1000 which are divisible by 3 is 83667.

A

83667

B

90000

C

83660

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
The required number are 3, 9, 15, …., 999.
Since, `l = a +(n-1)d`
` therefore " " 999 = 3 + (n-1) 6`
`rArr 6n = 1002 rArr n = 167`
`therefore S = (n)/(2)[a+l] = (167)/(2) [3 + 999]`
`= (167)/(2)(1002) = 83667`
Promotional Banner

Topper's Solved these Questions

  • PRACTICE SET 16

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Paper - 2 (MATHEMATICS )|50 Videos

  • PRACTICE SET 18

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2 (MATHEMATICS)|50 Videos

Similar Questions

Explore conceptually related problems

The sum of all odd numbers between 1 and 1000 which are divisible by 3 is

Find the sum of all integers between 0 and 500 which are divisible by 7.

Sum of all the numbers between 1 and 1000 which are divisible by 3 is

Find the sum of integers between 10 and 500 which are divisible by 7

Find the sum of all integers between 101 and 500, which are divisible by 9.

Find the sum of all integers between 100 and 50, which are divisible by 9.

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 17-MATHEMATICS
  1. Three digit numbers are formed with the digits 0,2,4,6 and 8. Write th...

    Text Solution

    |

  2. The angle betwene the line vecr=(1+2mu)hati+(2+mu)hatj+(2m-1)hatk and ...

    Text Solution

    |

  3. In triangle ABC, if ( a + b + c) (a-b+c) = 3 ac, then

    Text Solution

    |

  4. If cot x + cosec x = sqrt(3)x, then the principal value of (x-(pi)/(6)...

    Text Solution

    |

  5. The midpoint of the chord 4x-3y=5 of the hyperbola 2x^2-3y^2 = 12 is

    Text Solution

    |

  6. Show that the sum of all odd integers between and 1000 which are divis...

    Text Solution

    |

  7. The sum of infinity of the progression 9-3+1-(1)/(3)+… is

    Text Solution

    |

  8. Two finite sets A and 8 have m and n element respectively. If the tota...

    Text Solution

    |

  9. If A={1,2,3,4}" and "B={1,2,3,4,5,6} are two sets and function f: A to...

    Text Solution

    |

  10. The angle between the pair of straight lines y^(2)sin^(2)theta-xy sin^...

    Text Solution

    |

  11. A unit vector in xy-plane that makes an angle of 45^0 with the vector ...

    Text Solution

    |

  12. The function {{:(|x-3|,,ifxge1),((x^(2))/(2)-(3x)/(2)+(13)/(4),, if xl...

    Text Solution

    |

  13. if y = x + x^(2) + x^(3) + …oo, where |x| lt 1, then for |y| lt 1, (d...

    Text Solution

    |

  14. If "y"="tan"^(-1)"\ "[(sqrt(1+"x"^2-sqrt(1-"x"^2)))/(sqrt(1+"x"^2+)"\ ...

    Text Solution

    |

  15. For all values of theta,3-costheta+cos(theta+(pi)/(3)) lie in the inte...

    Text Solution

    |

  16. The value of cot(cosec^(-1)(5)/(3)+tan^(-1)""(2)/(3)) is

    Text Solution

    |

  17. The equation of pair of lines joining origin to the points of intersec...

    Text Solution

    |

  18. Three letters are written to different persons and addressess to three...

    Text Solution

    |

  19. A line makes acute angle of alpha, beta and gamma with the coordinate...

    Text Solution

    |

  20. The probability that number selected at random from that number 1, 2, ...

    Text Solution

    |