Home
Class 12
MATHS
If a, b, c form an A.P. and b, c, a form...

If a, b, c form an A.P. and b, c, a form a G.P., show that `(1)/(c ), (1)/(a), (1)/(b)` form an A.P.

Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 D (Multiple Choice Type Questions)|2 Videos

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 D (Very Short Answer Type Questions)|27 Videos

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 C (Short Answer Type Questions)|43 Videos

  • SECOND ORDER DERIVATIVE

    CHHAYA PUBLICATION|Exercise Sample Question for Competitive Examination (Assertion-Reason type)|2 Videos

  • SET THEORY

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

If a, b, c are In A.P., then show that, (1)/(b c), (1)/(c a), (1)/(a b) are in A.P.

If a. b, c are in A.P, then show that 1/(bc) , 1/(ca) , 1/(ab) are also in A.P.

If a, b, c, d are in A.P. and a, b, c, d are in G.P., show that a^(2) - d^(2) = 3(b^(2) - ad) .

If a^(2), b^(2), c^(2) are in A.P., prove that (1)/(b+c), (1)/(c+a), (1)/(a+b) are also in A.P.

If (b+c)/(a), (c+a)/(b), (a+b)/(c ) are in A.P. show that (1)/(a), (1)/(b), (1)/(c ) are also in A.P. (a+b+c != 0) .

If a, c, b are in A.P. and b, c, d are in G.P. prove that, b, (b-c), (d-a) are in G.P.

If a^2, b^2, c^2 are in A.P , then prove that 1/(b+c), 1/(c+a),1/(a+b) are in A.P

If a^(2), b^(2), c^(2) are in A.P., show that, (b+c), (c+a), (a+b) are in H.P.

If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+(1//a c),c+1//(a b) are also in A.P.

If a, b, c be in A.P. and x, y, z be in G.P., prove that, x^(b-c).y^(c-a).z^(a-b) = 1 .

CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 C (Long Answer Type Questions)
  1. If the A.M. of two numbers be twice their G.M., prove that two numbers...

    Text Solution

    |

  2. If A and G be the A.M. and G.M. of two numbers , show that the numbers...

    Text Solution

    |

  3. If a, b, c form an A.P. and b, c, a form a G.P., show that (1)/(c ), (...

    Text Solution

    |

  4. If the arithmetic mean of y and z be x and that of (1)/(x) and (1)/(y)...

    Text Solution

    |

  5. The sum of three numbers in A.P. is 15. If 1, 4 and 19 are added to th...

    Text Solution

    |

  6. The sum of three numbers in A.P. is 18. If 2, 2, 6 are added respectiv...

    Text Solution

    |

  7. Three terms are in G.P. Their product is 216. If 4 be added to the fir...

    Text Solution

    |

  8. Find the sum to n terms of each of the following series : 1 + 11 + 1...

    Text Solution

    |

  9. Find the sum to n terms of each of the following series : 2 + 22 + ...

    Text Solution

    |

  10. 0.8 + 0.88 + 0.888 + …

    Text Solution

    |

  11. Find the sum to n terms of each of the following series : 0.6 + 0.6...

    Text Solution

    |

  12. Find the sum to n terms of each of the following series : 1 + 4 + 1...

    Text Solution

    |

  13. Three unequal numbers a, b, c are in A.P. and a, (b-a), (c-a) are in G...

    Text Solution

    |

  14. If a, c, b are in A.P. and b, c, d are in G.P. prove that, b, (b-c), (...

    Text Solution

    |

  15. The first term of an A.P. is the same as that of a G.P., the common di...

    Text Solution

    |

  16. Find the sum to n terms : (1)/(2) + (3)/(2^(2)) + (5)/(2^(3)) +…+ (2...

    Text Solution

    |

  17. Find the sum to n terms : 2 + 3.3 + 4.3^(2) + 5.3^(3) +…

    Text Solution

    |

  18. Find the sum to n terms : 12 + 105 + 1008 + 10011+…

    Text Solution

    |

  19. Find the sum to n terms : 12 + 14 + 24 + 58 + 164+…

    Text Solution

    |

  20. The rth term of a series is (2r + 1)2^(r ), find the sum of first n te...

    Text Solution

    |