Home
Class 12
MATHS
If a, b, c are in G.P. and x, y be the A...

If a, b, c are in G.P. and x, y be the A.M. between a, b and b, c respectively, prove that,
`(a)/(x) + (c )/(y) = 2`

Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 C (Long Answer Type Questions)|35 Videos

  • SEQUENCE AND SERIES

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

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 C (Very Short Answer Type Questions)|17 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 G.P. and x, y be the A.M. between a, b and b, c respectively, prove that, (1)/(x) + (1)/(y) = (2)/(b)

If a,b,c are in G. P. and x, y are A.M. of a, b and b, c respectively, then the value of ((a)/(x)+ (c )/(y)) is-

If a,b,c are in G.P and x,y are the arithmetic mean of a and b aand b,c prove that a/x+c/y=2and 1/x+1/y=2/b.

If a, b, c are in GP and a, x, b, y are in AP Then prove that, a/x + c/y = 2

If a,b, and c are in G.P then a+b,2b and b+ c are in

If a, b, c are in GP and a, x, b,y, c ar in AP. then prove that, 1/x + 1/y = 2/b

If a, b, c are in AP, a, x, b are in GP , where as b, y and c also in GP. Then prove that x^2, b^2, y^2 are in AP.

If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmetic means between a ,b ,a n db ,c , then the value of a/x+c/y is 1 b. 2 c. 1//2 d. none of these

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

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.

CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 C (Short Answer Type Questions)
  1. Shri A. K. Roy borrows Rs. 6000 to repay the amount with interest of R...

    Text Solution

    |

  2. A man borrows Rs. 19682 without interest and agrees to repay the money...

    Text Solution

    |

  3. The A.M. of two numbers is 15 and their G.M. is 12. Find the numbers.

    Text Solution

    |

  4. If a, b, c are in G.P. and x, y be the A.M. between a, b and b, c resp...

    Text Solution

    |

  5. If a, b, c are in G.P. and x, y be the A.M. between a, b and b, c resp...

    Text Solution

    |

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

    Text Solution

    |

  7. The sum of three numbers in G.P. is 70. If each of the two extremes be...

    Text Solution

    |

  8. Let t(r) be the rth term of an A.P. If t(2), t(8) and t(32) are in G.P...

    Text Solution

    |

  9. If p, q, r be in arithmetic progression, then show that the pth, qth a...

    Text Solution

    |

  10. The nth term of a series is 3^(n) + 2n, find the sum of first n terms ...

    Text Solution

    |

  11. If one arithmetic mean A and two geometric means p, q be inserted betw...

    Text Solution

    |

  12. If A is the A.M. and G is the G.M. of two unequal positive real number...

    Text Solution

    |

  13. Between two positive real numbers a and b, one arithmetic mean A and t...

    Text Solution

    |

  14. If a, b, c are in G.P. and the equation ax^(2) + 2bx + c = 0 and dx^(2...

    Text Solution

    |

  15. If a is A.M. of two positive numbers b and c and two G.M's between b a...

    Text Solution

    |

  16. If G is the G.M. between two positive numbers a and b, show that (1)/(...

    Text Solution

    |

  17. If sum of the square of three different terms in G.P. is S^(2) their s...

    Text Solution

    |

  18. Show that sum of n G.M.s between a and b is ((ab^((1)/(n+1))-ba^((1)/(...

    Text Solution

    |

  19. Evaluate : Sigma(K=1)^(7) [((1)/(5))^(2K+1).(7)^(K-1)]

    Text Solution

    |

  20. The A.M. between m and n and the G.M. between a and b are each equal t...

    Text Solution

    |