Home
Class 12
MATHS
If a, b, c are in HP, then (a-b)/(b-c) i...

If a, b, c are in HP, then `(a-b)/(b-c)` is equal to

Text Solution

Verified by Experts

Since, `a,b,c` are in HP, therefore
`(1)/(a),(1)/(b),(1)/(c)` are in AP
`i.e.(1)/(b)-(1)/(a)=(1)/(c)-(1)/(b)`
or `(a-b)/(ab)=(b-c)/(bc)" or "(a-b)/(b-c)=(a)/(c)`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise For Session 2|11 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

(A uu B)^(c) is equal to :

If a, b, c are in HP., then a/(b+c),b/(c+a),c/(a+b) are in

If a ,b ,c are in G.P. and a-b ,c-a ,a n db-c are in H.P., then prove that a+4b+c is equal to 0.

If a,b,c are in HP, then prove that (a+b)/(2a-b)+(c+b)/(2c-b)gt4 .

a, b, c are three vectors, such that a+b+c=0 ,|a|=1, |b|=2, |c|=3, then a*b+b*c+c*a is equal to

If the quadratic equations, a x^2+2c x+b=0 and a x^2+2b x+c=0(b!=c) have a common root, then a+4b+4c is equal to:

If a,b,c are in AP and a^(2),b^(2),c^(2) are in HP, then

If b-c,2b-lambda,b-a " are in HP, then " a-(lambda)/(2),b-(lambda)/(2),c-(lambda)/(2) are in

If a,b,c are in HP, then prove that sin ^(2) ""(A)/(2), sin ^(2) ""(B)/(2), sin ^(2) ""(C )/(2) are also in HP.

If a, b and c are non-coplanar vectors and d=lambda vec a+mu vec b+nu vec c , then lambda is equal to

ARIHANT MATHS-SEQUENCES AND SERIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If a, b, c are in HP, then (a-b)/(b-c) is equal to

    Text Solution

    |

  2. Let a,b,c be in A.P. and |a|lt1,|b|lt1|c|lt1.ifx=1+a+a^(2)+ . . . ."to...

    Text Solution

    |

  3. Evluate int (tan^(-1)x)/(1+x^2) dx

    Text Solution

    |

  4. If a1, a2, a3, be terms of an A.P. and (a1+a2+.....+ap)/(a1+a2+.....+...

    Text Solution

    |

  5. If a1, a2, a3,.....an are in H.P. and a1 a2+a2 a3+a3 a4+.......a(n-1...

    Text Solution

    |

  6. Let V(r ) denotes the sum of the first r terms of an arithmetic progre...

    Text Solution

    |

  7. Let Vr denote the sum of the first r terms of an arithmetic progressio...

    Text Solution

    |

  8. Let V(r ) denotes the sum of the first r terms of an arithmetic progre...

    Text Solution

    |

  9. LetA(1),G(1),H(1) denote the arithmetic, geometric and harmonic means ...

    Text Solution

    |

  10. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

    Text Solution

    |

  11. LetA(1),G(1),H(1) denote the arithmetic, geometric and harmonic means ...

    Text Solution

    |

  12. In a G.P of positive terms if any term is equal to the sum of the next...

    Text Solution

    |

  13. Suppose four distinct positive numbers a(1),a(2),a(3),a(4) are in G.P....

    Text Solution

    |

  14. The first two terms of a geometric progression add up to 12. The sum o...

    Text Solution

    |

  15. If the sum of first n terms of an A.P. is cn^(2) then the sum of squar...

    Text Solution

    |

  16. The sum to infinity of the series 1+2/3+6/3^2+14/3^4+...is

    Text Solution

    |

  17. Let Sk,k=1, 2, …. 100 denote the sum of the infinite geometric series ...

    Text Solution

    |

  18. Let a1, a2, a3, ,a(11) be real numbers satisfying a1=15 , 27-2a2>0 an...

    Text Solution

    |

  19. Check 2,4,6,8,10 are in A.P or not

    Text Solution

    |

  20. The minimum value of the sum of real numbers a^-5, a^-4, 3a^-3, 1,a^8 ...

    Text Solution

    |

  21. A man saves ₹ 200 in each of the first three months of his servies.In ...

    Text Solution

    |