Home
Class 12
MATHS
In an A.P., if p^(th) term is 1/q and q^...

In an A.P., if `p^(th)` term is `1/q` and `q^(th)` term is `1/p`, prove that the sum of first `pq` terms is `1/2(pq + 1)`, where `p != q`

Text Solution

Verified by Experts

The correct Answer is:
` = 1/2 (pq + 1)`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|49 Videos

  • SEQUENCES AND SERIES

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|105 Videos

  • RELATIONS AND FUNCTIONS

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|33 Videos

  • SETS

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|21 Videos

Similar Questions

Explore conceptually related problems

In an A.P. if p^(th) term is 1/q and q^(th) term is 1/p , prove that the sum of first pq terms is 1/2(pq+1) , where p ne q .

If p^(th) term of an AP is q and q^(th) term is p, find (p+q)^(th) term.

In an A.P. 19^(th) term is 52 and 38^(th) term is 128, Find sum of first 56 terms.

The A.P. in which 4^(th) term -15 and 9^(th) term is -30. Find the sum of first 10 numbers.

In an A.P. if m^("th") term is n and the n^("th") term is m, where m ne n , find the pth term .

If the first term of a G.P. is 729 and its 7^(th) term is 64, then the sum of first seven terms is

In an A.P. 10^(th) term is 46, sum of 5^(th) and 7^(th) term is 52. find the A.P.

The pth term of an A.P. is a and qth term is bdot Then find the sum of its (p+q) terms.

NEW JOYTHI PUBLICATION-SEQUENCES AND SERIES -QUESTIONS FROM COMPETITIVE EXAMS
  1. In an A.P., if p^(th) term is 1/q and q^(th) term is 1/p, prove that t...

    Text Solution

    |

  2. The sum to n terms of the series 1/2 + 3/4 + 7/8 + 15/16 + ....... is

    Text Solution

    |

  3. 0.2 + 0.22 + 0.222 + …….. to n terms =

    Text Solution

    |

  4. If (a^(n + 1) + b^(n + 1))/(a^(n) + b^(n)) is the arithmetic mean betw...

    Text Solution

    |

  5. If (i)^(2) = -1, (i)^(2) + (i)^(4) + (i)^(6) + ...... to (2n + 1) term...

    Text Solution

    |

  6. If S(n) denotes the sum of n terms of an A.P., S(n +3) - 3S(n + 2) + 3...

    Text Solution

    |

  7. The HM of 2 numbers is 4. Their AM is A and GM is G. If G satisfies 2...

    Text Solution

    |

  8. The angle of triangle are in 30^(@). The greatest angle in radians is

    Text Solution

    |

  9. How many terms of the geometric series 1 + 4 + 16 + 64 + ……… will make...

    Text Solution

    |

  10. Find the value of n so that (a^(n+1)+b^(n+1))/(a^(n)+b^n) may be the ...

    Text Solution

    |

  11. The sum of the series 1 + 2.2 + 3.2^(2) + 4.2^(3) + 5.2^(4) + ……… + 1...

    Text Solution

    |

  12. If A, G, H denote respectively the AM, GM and HM between two unequal p...

    Text Solution

    |

  13. Let a, b, c be district real numbers. If a, b, c are in G.P and a + b ...

    Text Solution

    |

  14. The numbers of terms of the A.P 3, 7, 11, 15, …… to be taken so that t...

    Text Solution

    |

  15. If the progression 3, 10, 17, …… and 63, 65, 67, …… are such that thei...

    Text Solution

    |

  16. Which term of the geometric sequence 5,2,4/5 , 8/(25) … is (128)/(15...

    Text Solution

    |

  17. If a, b and c are respectively the p^(th),q^(th)and r^(th) terms of an...

    Text Solution

    |

  18. The sum of infinite terms of the geometric progression (sqrt(2) + 1)/(...

    Text Solution

    |

  19. The two geometric means between the numbers 1 and 64 are

    Text Solution

    |

  20. If 1 + (1 + 2)/2 + (1 + 2 + 3)/3 + ...... to n terms is s, then s is e...

    Text Solution

    |

  21. If a, b, and c are in A.P., then which one of thew following is not tr...

    Text Solution

    |