Home
Class 11
MATHS
The sum of the first p , q , r terms of ...

The sum of the first `p , q , r` terms of an A.P. are `a , b , c` respectively. Show that `a/p(q-r)+b/q(r-p)+c/r(p-q)=0`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    RD SHARMA ENGLISH|Exercise All Questions|228 Videos

Similar Questions

Explore conceptually related problems

Sum of the first p, q and r terms of an A.P are a, b and c, respectively.Prove that a/p(q-r)+b/q(r-p)+c/r(p-q)=0

Sum of the first p, q and r terms of an A.P are a, b and c, respectively.Prove that a/p(q-r)+b/q(r-p)+c/r(p-q)=0

The sums of first p, q, r terms of an A.P. are a, b, c respectively. Prove that (a)/(p) (q-r) +(b)/(q) (r-p) +(c )/(r) (p-q) =0

If pth,qth and rth terms of an A.P. are a, b, c respectively, then show that (i) a(q-r)+b(r-p)+c(p-q)=0

The p^(t h),q^(t h) and r^(t h) terms of an A.P. are a, b, c, respectively. Show that (q-r)a+(r-p)b+(p-q)c=0 .

If the p^(t h) , q^(t h) and r^(t h) terms of a GP are a, b and c, respectively. Prove that a^(q-r)b^(r-p)c^(p-q)=1 .

If pth, qth, and rth terms of an A.P. are a ,b ,c , respectively, then show that (1) a(q-r)+b(r-p)+c(p-q)=0 (2)(a-b)r+(b-c)p+(c-a)q=0

If pth, qth, and rth terms of an A.P. are a ,b ,c , respectively, then show that (a-b)r+(b-c)p+(c-a)q=0

If pth, qth, and rth terms of an A.P. are a ,b ,c , respectively, then show that (a-b)r+(b-c)p+(c-a)q=0

If the p t h ,\ q t h\ a n d\ r t h terms of a G.P. are a ,\ b ,\ c respectively, prove that: a^((q-r))dot^b^((r-p))dotc^((p-q))=1.

RD SHARMA ENGLISH-ARITHMETIC PROGRESSIONS-All Questions
  1. How many terms of the series 54,51, 48,.. be taken so that their sum i...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. The ratio of the sum of m and n terms of an A.P. is m^2: n^2dot Show t...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. Find the sum of the following series: 101+99+97+....+47

    Text Solution

    |

  19. Find the sum of the following series: (a-b)^2+(a^2+b^2)+(a+b)^2+...+[(...

    Text Solution

    |

  20. Find the sum of first n natural numbers.

    Text Solution

    |