Home
Class 12
MATHS
The A.M. and H.M. between two numbers ar...

The A.M. and H.M. between two numbers are 27 and 122, respectively, then find their G.M.

Text Solution

Verified by Experts

Let A,G and H denote, respectively the A.M.,G.M., and H.M. between the two numbers. Then, A=27 and H=12. Since A,G, and H are in G.P. Therefore,
`G^(2)=AH=27xx12`
`rArrG=18`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.1|3 Videos
  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.2|10 Videos
  • PROGRESSION AND SERIES

    CENGAGE|Exercise Single correct Answer|54 Videos
  • PROBABILITY II

    CENGAGE|Exercise NUMARICAL VALUE TYPE|2 Videos
  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

If the AM and HM of two numbers are 27 and 12 respectively, then what is their GM equal to ?

If the A.M. and G.M. of two numbers are 16 and 12 respectively find their H.M.

If A.M. and G.M. of two numbers is 10 and 8 respectively then find their H.M.

G.M and H.M of two numbers are 10 and 8 respectively.The numbers are

The A.M and G.M of two numbers a and b are 18 and 6 respectively then H.M of a and b is

CENGAGE-PROGRESSION AND SERIES-Examples
  1. If nine arithmetic means and nine harmonic means are inserted between ...

    Text Solution

    |

  2. Let a ,b be positive real numbers. If a A1, A2, b be are in arithmetic...

    Text Solution

    |

  3. The A.M. and H.M. between two numbers are 27 and 122, respectively, ...

    Text Solution

    |

  4. If the A.M. between two numbers exceeds their G.M. by 2 and the GM. ...

    Text Solution

    |

  5. Find the sum 2017+1/4(2016+1/4(2015+…+1/4(2+1/4(1))..))

    Text Solution

    |

  6. The sum of 50 terms of the series 1+2(1+1/(50))+3(1+1/(50))^2+ is give...

    Text Solution

    |

  7. Find the sum to ininity of the series 1-3x+5x^2+7x^3+..... oo when Ix|...

    Text Solution

    |

  8. The sum of the infinite series 1+(1+1/5)(1/2)+(1+1/5+1/(5^2))(1/(2^2))...

    Text Solution

    |

  9. If the sum to infinity of the series 3+(3+d)1/4+(3+2d)1/(4^2)+oo is (4...

    Text Solution

    |

  10. Find the sum to infinity of the series 1^2+2^2+3^2+4^2+oodot

    Text Solution

    |

  11. Find the sum 2xx5+5xx9+8xx13+11xx17+.. n terms.

    Text Solution

    |

  12. Find the sum of the series 1xxn+2(n-1)+3xx(n-2)++(n-1)xx2+nxx1.

    Text Solution

    |

  13. For and odd integer n ge 1, n^(3) - (n - 1)^(3) + …… + (- 1)^(n-1) ...

    Text Solution

    |

  14. Find the sum of the series (1^3)/1+(1^3+2^3)/(1+3)+(1^3+2^3+3^3)/(1+3+...

    Text Solution

    |

  15. Find the sum of first n terms of the series 1^3+3xx2^2+3^3+3xx4^2+5^3+...

    Text Solution

    |

  16. If Sigma(r=1)^(n) T(r)=n(2n^(2)+9n+13), then find the sum Sigma(r=1)^(...

    Text Solution

    |

  17. Find the sum to n terms of the series 3+15+35+63+

    Text Solution

    |

  18. Find the sum of the following series to n terms 5+7+13+31+85+

    Text Solution

    |

  19. Find the sum(k=1)^(oo) sum(n=1)^(oo)k/(2^(n+k)).

    Text Solution

    |

  20. The sum of the products of the ten numbers +-1,+-2,+-3,+-4,+-5 taking ...

    Text Solution

    |