Home
Class 11
MATHS
If mth, nth and pth terms of a G.P. form...

If mth, nth and pth terms of a G.P. form three consecutive terms of a G.P. Prove that `m ,n ,a n dp` form three consecutive terms of an arithmetic system.

Text Solution

Verified by Experts

The correct Answer is:
A.P.
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise CHECK YOUR UNDERSTANDING|10 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise COMPETITION FILE|21 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise EXERCISE|7 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise Chapter Test|11 Videos

  • SETS

    MODERN PUBLICATION|Exercise CHAPTER TEST 1|12 Videos

Similar Questions

Explore conceptually related problems

If mth,nth and pth terms of a G.P.form three consecutive terms of a Grove that m,n, and p form three consecutive terms of an arithmetic system.

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

If second third and sixth terms of an A.P.are consecutive terms o a G.P.write the common ratio of the G.P.

If 2nd, 3rd and 6th terms of an AP are the three consecutive terms of a GP then find the common ratio of the GP.

If the sum of three consecutive terms of a G.P. is 38 and their product is 1728, then find these three consecutive terms.

If (1)/(a+b),(1)/(2b),(1)/(b+c) are three consecutive terms of an A.P.prove that a,b,c are the three consecutive terms of a G.P.

If a,b, and c are three consecutive terms of an A.P, prove that k^(a),k^(b) and k^(c) are three consecutive terms of a G.P. Assume k to be a non zero real number.

For what value of p, the following terms are three consecutive terms of an A.P. 4/5 , p,2.

nth term of a G.P. is a + (n – 1)d.

MODERN PUBLICATION-SEQUENCES AND SERIES-REVESION EXERCISE
  1. If a, b, c are in A.P., prove that a^(3)+4b^(3)+c^(3)=3b(a^(2)+c^(2)).

    Text Solution

    |

  2. If a^2(b+c),b^2(c+a),c^2(a+b), are in A.P. show that either a ,b ,c ar...

    Text Solution

    |

  3. If mth, nth and pth terms of a G.P. form three consecutive terms of a ...

    Text Solution

    |

  4. If x,y,z are in G.P and a^x=b^y=c^z,then

    Text Solution

    |

  5. We are given two G.P's one with the first term a and common ratio r an...

    Text Solution

    |

  6. if sn, denotes the sum of n terms of a GP whose first term and common ...

    Text Solution

    |

  7. If p, q, r are in G.P. and the equations, p x^2+2q x+r=0and dx^2+2e x...

    Text Solution

    |

  8. If S(n) denotes the sum of n terms of a G.P., prove that: (S(10)-S(20)...

    Text Solution

    |

  9. The sum of the first thre consecutive terms of G.P is 13 and the sum o...

    Text Solution

    |

  10. If 1/(a+b)+1/(b+c)=1/b, prove that a,b,c are in G.P.

    Text Solution

    |

  11. 150 workers were engaged to finish a job in a certain number of days. ...

    Text Solution

    |

  12. If |x|<1a n d|y|<1, find the sum of infinity of the following series: ...

    Text Solution

    |

  13. A manufacture reckons that the value of a machine which costs him Rs. ...

    Text Solution

    |

  14. The sum of the series : 1+1/(1+2)+1/(1+2+3)+...... upto 10 terms is :

    Text Solution

    |

  15. Find the sum of the series: 1. n+2.(n-1)+3.(n-2)++(n-1). 2+n .1.

    Text Solution

    |

  16. Obtain the sum of the series 1/4+1/16+1/64……………….to oo

    Text Solution

    |

  17. Show that (1xx2^2+2xx3^2+dotdotdot+nxx(n+1)^2)/(1^2xx2+2^2xx3+dotdotdo...

    Text Solution

    |

  18. What will Rs. 500 amounts to in 10 years after its deposit in a bank w...

    Text Solution

    |

  19. A man deposited Rs 10000 in a bank at the rate of 5% simple interes...

    Text Solution

    |

  20. If a1,a2,a3, ,an are in A.P., where ai >0 for all i , show that 1/(sqr...

    Text Solution

    |