Home
Class 11
MATHS
If the m^(t h) term of an A.P. is 1/n a ...

If the `m^(t h)` term of an A.P. is `1/n a n d\ t h e\ n^(t h)t e r m\ i s1/m ,\ ` show that the sumof `m n` terms is `1/2(m n+1)` where `m!=ndot`

Text Solution

Verified by Experts

Let sum be a
SO,
`a_{m}=a+(m-1) d=1 / n ldots ldots . .(1)`
nth term `=1 / {m}`
`a_{n}=a+(n-1) d=1 / m ldots ldots . .(2)` ...
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    RD SHARMA|Exercise Solved Examples And Exercises|228 Videos

Similar Questions

Explore conceptually related problems

If the m^(th) term of an A.P.is (1)/(n) and the n^(th) term is (1)/(m), show that the sum of mn terms is (1)/(2)(mn+1)

If the m^(th) term of an A.P.is (1)/(n) and the n^(th) terms is (1)/(m), show that the sum of mn terms is (1)/(2)(mm+1)

If the m^(th) term of an H.P. is n and the n^(th) term is m, show that its (mm)^(th) term is 1.

The m^(th) term of an A.P. is n and n^(th) term is m its p^(th) term is

If the mth term of an AP is a and its nth term is b, show that the sum of its ( m +n) " term is " ((m +n))/2 . {a +b+ (( a-b))/((m-n))}

If the m^(th) term of a H.P.be n and n^(th) term be m,then the r^(th) term will be:

If m times the m^(th) term of an A.P. is equal to n times its n^(th) term , then show that (m+n)^(th) term of the A.P. is zero .

The sum of the first n terms of an A.P. is 3n^2+6n . Find the n t h term of this A.P.

RD SHARMA-ARITHMETIC PROGRESSIONS-Solved Examples And Exercises
  1. If the sum of n terms of an A.P. is 3n^2+5n and its mth term is 164, f...

    Text Solution

    |

  2. Find the sum of n terms of the sequence (an),w h e r ean=5-6n ,n in N...

    Text Solution

    |

  3. If the m^(t h) term of an A.P. is 1/n a n d\ t h e\ n^(t h)t e r m\ i ...

    Text Solution

    |

  4. How many terms of the series 54,51, 48,.. be taken so that their sum i...

    Text Solution

    |

  5. solve: 1 + 6 + 11 + 16 +.........+ x = 148

    Text Solution

    |

  6. The sum of the first p , q , r terms of an A.P. are a , b , c respecti...

    Text Solution

    |

  7. If the sum of first m terms of an A.P. is the same as the sum of its f...

    Text Solution

    |

  8. The ratio of the sum of ma n dn terms of an A.P. is m^2: n^2dot Show t...

    Text Solution

    |

  9. The interior angles of a polygon are in A.P. the smallest angle is 120...

    Text Solution

    |

  10. Prove that a sequence in an A.P., if the sum of its n terms is of the ...

    Text Solution

    |

  11. If the first term of an A.P. is 2 and the sum of first five terms is ...

    Text Solution

    |

  12. The sum of n terms of two arithmetic progressions are in the ratio (3n...

    Text Solution

    |

  13. Let Sk be the sum of first k terms of an A.P. What must this progressi...

    Text Solution

    |

  14. Find the sum of the following arithmetic progression: 50,46,42,… upto ...

    Text Solution

    |

  15. Find the sum of the following series : (i) 1,3,5,7...upto 12 terms.

    Text Solution

    |

  16. Find the sum of the following arithmetic progression: 3,9/2,6,15/2,…...

    Text Solution

    |

  17. Find the sum of the following arithmetic progression: 41,36,31,…….to 1...

    Text Solution

    |

  18. Find the sum of the following arithmetic progression: a+b ,\ a-b ,\...

    Text Solution

    |

  19. Find the sum of the following arithmetic progression: (x-y)/(x+y),(3x-...

    Text Solution

    |

  20. Find the sum of the following series: 2+5+8+. . . .+182

    Text Solution

    |