Home
Class 11
MATHS
If a, b, care in GP then prove that a^3,...

If `a, b, c`are in GP then prove that `a^3, b^3, c^3` are in GP.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.

If a,b, c are in GP, Prove that a^2, b^2 , c^2 are in GP.

If a,b,c are in GP Then prove that, loga ,logb , logc are in AP.

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

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, 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,b,c,d are in GP then prove that, (a^2-b^2), (b^2-c^2), (c^2-d^2) are in GP.

If a, b, c are in A.P., b, c, d are in G.P. and 1/c ,""1/d ,""1/e are in A.P. prove that a, c, e are in G.P.

If a ,b ,c ,d are in G.P., then prove that (a^3+b^3)^(-1),(b^3+c^3)^(-1),(c^3+d^3)^(-1) are also in G.P.

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.

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. If a,b,c,d are in GP then prove that, (a^2-b^2), (b^2-c^2), (c^2-d^2)...

    Text Solution

    |

  2. If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx ,...

    Text Solution

    |

  3. If a, b, care in GP then prove that a^3, b^3, c^3 are in GP.

    Text Solution

    |

  4. The second term of an H.P. is 3/14 and the fifth term is 1/10 . Find...

    Text Solution

    |

  5. A pack contains n cards numbered from 1 to n. Two consecutive numbered...

    Text Solution

    |

  6. If the sixth term of an H.P. is 10 and the 11th term is 18 Find the 16...

    Text Solution

    |

  7. If he equation x^3+a x^2+b x+216=0 has three real roots in G.P., then ...

    Text Solution

    |

  8. Let Tr be the rth term of an A.P., for r=1,2,3,..... If for some pos...

    Text Solution

    |

  9. Let An = (3/4) -(3/4)^2 + (3/4)^3 +.....+(-1)^(n - 1) (3/4)^n , Bn = 1...

    Text Solution

    |

  10. For a positive integer n let a(n)=1+1/2+1/3+1/4+.......+1/((2^n)-1) th...

    Text Solution

    |

  11. If x >1,y >1,a n dz >1 are in G.P., then 1/(1+lnx),1/(1+l ny)a n d1/(1...

    Text Solution

    |

  12. Compute the 100th term of HP if the 10th and 20th term of HP are 20 an...

    Text Solution

    |

  13. Find the 6th and nth term of the GP 2, 6, 18, 54,.....

    Text Solution

    |

  14. If a,b,c are in AP and a^2,b^2,c^2 are in HP, then

    Text Solution

    |

  15. Let a ,b be positive real numbers. If a, A1, A2, b be are in arithmeti...

    Text Solution

    |

  16. The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, ...

    Text Solution

    |

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

    Text Solution

    |

  18. If y^2=x za n da^x=b^y=c^z , then prove that (log)6a=(log)c bdot

    Text Solution

    |

  19. The geometric mean between -9 and -16 is a.12 b. -12 c. -13 d. none of...

    Text Solution

    |

  20. The value of 0.568 x 4.9 =?

    Text Solution

    |