Home
Class 11
MATHS
If a ,b ,c,d are in G.P. prove that (a^...

If `a ,b ,c,d` are in G.P. prove that `(a^n+b^n),(b^n+c^n),(c^n+d^n)` are in G.P.

Text Solution

Verified by Experts

Given, `a ,b ,c, d` are in G.P.

Geometric mean relation:

`b^2=ac`

`c^2=bd`

`bc=ad`

`b/a=c/b=d/c`


To prove: `(a^n+b^n),(b^n+c^n),(c^n+d^n)` are in G.P.

To prove: `(b^n+c^n)^2=(a^n+b^n)(c^n+d^n)`


...
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|157 Videos

  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|5 Videos

Similar Questions

Explore conceptually related problems

If a,b,c,d are in G.P.prove that (a^(n)+b^(n)),(b^(n)+c^(n)),(c^(n)+a^(n)) are in G.P.

If a,b,c are in G.P.,then prove that log a^(n),log b^(n),log c^(n)quad are in A.P.

If a,b,c,d are in G.P.,prove that a+b,b+c,c+d are also in G.P.

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

If a, ,b c, are in G.P., then log_(a) n, log_(b) n, log_(c) n are in

If a, b, c, d are in G.P., then prove that: (b-c)^(2)+(c-a)^(2)+(d-b)^(2)=(a-d)^(2)

If a, x, b as well as c, x, d are in GP while a^2,y,b^2 as well as c^2,y,d^2 are in AP then prove that a^n+b^n=c^n+d^n where n is an even integer or a^n+b^n+c^n+d^n=0 where n is an odd integer.

If l n(a+c),l n(a-c)a n dl n(a-2b+c) are in A.P., then (a) a ,b ,c are in A.P. (b) a^2,b^2, c^2, are in A.P. (c) a ,b ,c are in G.P. d. (d) a ,b ,c are in H.P.

RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  1. If a ,b, c ,d are in G.P, then (b-c)^2+(c-a)^2+(d-b)^2 is equal to

    Text Solution

    |

  2. If a ,\ b ,\ c ,\ d are in G.P., show that: (a b+b c+c d)^2=(a^2+b^2+c...

    Text Solution

    |

  3. If a ,b ,c,d are in G.P. prove that (a^n+b^n),(b^n+c^n),(c^n+d^n) are...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. If a , b , c are in G.P. prove that loga , logb , logc are in A.P.

    Text Solution

    |

  7. If a ,\ b ,\ c are in G.P. prove that 1/((log)a m),1/((log)b m),1/((lo...

    Text Solution

    |

  8. Find k such that k+9, k-6 and 4 from three consecutive terms of a G.P.

    Text Solution

    |

  9. Three numbers are in A.P. and their sum is 15. If 1,3,9 be added to th...

    Text Solution

    |

  10. The sum of three numbers which are consecutive terms of an A.P. is 21....

    Text Solution

    |

  11. The sum of three numbers in G.P. is 56. If we subtract 1,7,21 from the...

    Text Solution

    |

  12. If a ,\ b\ c are in G.P., prove that the following are also in G.P.: a...

    Text Solution

    |

  13. If a , b, c are in G.P., prove that the following are also in G.P.: a^...

    Text Solution

    |

  14. If a, b, c are in G. P., prove that a^2+ b^2, ab + bc, b^2 +c^2 are al...

    Text Solution

    |

  15. If (a-b),\ (b-c),(c-a) are in G.P. then prove that (a+b+c)^2=3(a b+b c...

    Text Solution

    |

  16. If the 4th, 10th and 16th terms of a G.P. are x, y, and z respectivel...

    Text Solution

    |

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

    Text Solution

    |

  18. If the pth, qth, rth, and sth terms of an A.P. are in G.P., then p-q ,...

    Text Solution

    |

  19. If a ,\ b ,\ c are in A.P. b ,\ c ,\ d are in G.P. and 1/c ,1/d ,1/e a...

    Text Solution

    |

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

    Text Solution

    |