Home
Class 11
MATHS
If x,y, z are three consecutive terms of...

If x,y, z are three consecutive terms of a G.P. then prove that `(1)/(x+y) + (1)/(y+ z)= (1)/(y)`.

Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    KUMAR PRAKASHAN|Exercise Exercise: 9.1|14 Videos

  • SEQUENCE AND SERIES

    KUMAR PRAKASHAN|Exercise Exercise: 9.2|18 Videos

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Question of Module)|16 Videos

  • SETS

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE|28 Videos

Similar Questions

Explore conceptually related problems

AB, CD, PQ are perpendicular to BD. If AB = x, CD = y and PQ = z prove that (1)/(x) + (1)/(y) = (1)/(z)

If x,y,z be three positive prime numbers. The progression in which sqrt(x),sqrt(y),sqrt(z) can be three terms (not necessarily consecutive) is

If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in GP.

If x , y , z are all different real numbers, then 1/((x-y)^2)+1/((y-z)^2)+1/((z-x)^2)=(1/(x-y)+1/(y-z)+1/(z-x))^2

For all positive numbers x,y,z the product ((1)/(x+y+z))((1)/(x)+(1)/(y)+(1)/(z))((1)/(xy+yz+zx))((1)/(xy)+(1)/(yz)+(1)/(zx)) equals

If x=1+(log)_a b c , y=1+(log)_b c a and z=1+(log)_c a b , then prove that x y z=x y+y z+z x

If y_1 and y_2 are the solution of the differential equation (dy)/(dx)+P y=Q , where P and Q are functions of x alone and y_2=y_1z , then prove that z=1+cdote^(-intQ/(y_1)dx), where c is an arbitrary constant.

If x, y, z are in arithmetic progression and a is the arithmetic mean of x and y and b is the arithmetic mean of y and z, then prove that y is the arithmetic mean of a and b.

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

KUMAR PRAKASHAN-SEQUENCE AND SERIES-Solutions of NCERT Exemplar Problems -Question of Module
  1. If x,y, z are three consecutive terms of a G.P. then prove that (1)/(x...

    Text Solution

    |

  2. The terms 1,1,2,3,5,8,13,……respresents which sequence?

    Text Solution

    |

  3. Which is the sequence whose terms are not finite?

    Text Solution

    |

  4. What does a(1) + a(2) + a(3) + …..+ a(n) represent

    Text Solution

    |

  5. Give new series by adding 2 in each term of arithmetic sequence 2,4,6,...

    Text Solution

    |

  6. Find twelveth term of A.P. 4, 8, 12…….

    Text Solution

    |

  7. 3 + 6+ 9 +…….Find sum of n terms.

    Text Solution

    |

  8. 4 + 8 + 12+…….Find sum of first 15 terms.

    Text Solution

    |

  9. Obtain arithmetic mean of 2 and 128

    Text Solution

    |

  10. Insert 5 arithmetic mean between 3 and 4.

    Text Solution

    |

  11. Find 8^(th) term of geometric sequence 3, 6,12,….

    Text Solution

    |

  12. Find n^(th) term of Geometric sequence 1,3,9,27,……

    Text Solution

    |

  13. Find S(n) for geometric sequence 4, 8, 15, 32,……

    Text Solution

    |

  14. Find sum of first 10 terms of geometric series 3,9, 27,……

    Text Solution

    |

  15. Find geometric mean of numbers 5 and 125.

    Text Solution

    |

  16. Insert 3 geometric mean between 4 and 64.

    Text Solution

    |

  17. The arithmetic and geometric mean of two positive numbers are 8 and 4 ...

    Text Solution

    |

  18. If A and G be A.M. and G.M., respectively between two positive numbers...

    Text Solution

    |

  19. Find value : 5^(2) + 6^(2) + 7^(2)+ …….+ 25^(2)

    Text Solution

    |

  20. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |