Home
Class 11
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 ne q`.

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    NCERT BANGLISH|Exercise EXERCISE 9.3|32 Videos

  • SEQUENCES AND SERIES

    NCERT BANGLISH|Exercise EXERCISE 9.4|10 Videos

  • SEQUENCES AND SERIES

    NCERT BANGLISH|Exercise EXERCISE 9.1|14 Videos

  • RELATIONS AND FUNCTIONS

    NCERT BANGLISH|Exercise Miscellaneous Exercise on Chapter 2|12 Videos

  • SETS

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 1|26 Videos

Similar Questions

Explore conceptually related problems

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 .

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

The nth term of an A.P. is p, show that, the sum of its first (2n-1) terms is (2n-1)p.

The first term of G.P. is 27 and 8th term is 1/81 . Find the sum of its first 10 terms.

if the Pth term of an A.P. is q and qth term is P.Then show that the nth term is p+q-n

The nth term of an A.P. is p and the sum of its first n terms is q. Prove that its first term is (1)/(n)(2q-p n) .

The sum of first p terms of an A.P. is (p^(2))/(n) and the sum of its first q(!= p) terms is (q^(2))/(n) . Show that the sum of its first n terms will be n.

If the pth term of an A.P. is q and the qth term is p , then find its rth term.

If the P^(th) and q^(th) terms of an A.Pare a and b respectively,then show that the sum of first (p+q) terms of thath A.P is 1/2(p+q) (a+b+(a-b)/(p-q))

The third term of an A.P. is (1)/(5) and the 5th term is (1)/(3) . Show that the sum of 15 terms of the A.P. is 8.

NCERT BANGLISH-SEQUENCES AND SERIES-EXERCISE 9.2
  1. Find the sum of odd integers from 1 to 2001.

    Text Solution

    |

  2. Find the sum of all natural numbers lying between 100 and 1000, which ...

    Text Solution

    |

  3. In an A.P., the first term is 2 and the sum of the first five terms is...

    Text Solution

    |

  4. How many terms of the A.P. – 6, , - (11)/2 , -5 ......... are needed t...

    Text Solution

    |

  5. In an A.P. if p^(th) term is 1/q and q^(th) term is 1/p , prove that t...

    Text Solution

    |

  6. If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 1...

    Text Solution

    |

  7. Find the sum to n terms of the A.P., whose k^("th") term is 5k + 1.

    Text Solution

    |

  8. If the sum of n terms of an A.P. is (pn + qn^2) , where p and q are co...

    Text Solution

    |

  9. The sums of n terms of two arithmetic progressions are in the ratio 5n...

    Text Solution

    |

  10. If the sum of first p terms of an A.P. is equal to the sum of the firs...

    Text Solution

    |

  11. Sum of the first p, q and r terms of an A.P. are a, b and c, respectiv...

    Text Solution

    |

  12. The ratio of the sums of m and n terms of an A.P. is m^2 : n^2. Show ...

    Text Solution

    |

  13. If the sum of n terms of an A.P. is 3n^2 + 5n and its m^("th") term ...

    Text Solution

    |

  14. Insert five numbers between 8 and 26 such that the resulting sequence ...

    Text Solution

    |

  15. If (a^(n)+b^n)/ (a^(n-1) +b^(n-1)) is the A.M. between a and b, then f...

    Text Solution

    |

  16. Between 1 and 31, m numbers have been inserted in such a way that t...

    Text Solution

    |

  17. A man starts repaying a loan as first instalment of Rs. 100. If he inc...

    Text Solution

    |

  18. The difference between any two consecutive interior angles of a polygo...

    Text Solution

    |