Home
Class 11
MATHS
If a ,b ,ca n dd are in H.P., then prove...

If `a ,b ,ca n dd` are in H.P., then prove that `(b+c+d)//a ,(c+d+a)//b ,(d+a+b)//c` and `(a+b+c)//d` , are in A.P.

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 a,b,c,d are in GP then prove thst (b+c)(b+d) =(c+a)(c+d)

If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+(1//a c),c+1//(a b) are also in A.P.

If a^2, b^2, c^2 are in A.P , then prove that 1/(b+c), 1/(c+a),1/(a+b) are in A.P

If a, b, c are in H.P., prove that, a(b+c), b(c+a), c(a+b) are in A.P.

a,b and c are in A.P. Prove that b+c , c+a and a+b are in A.P.

If a, b, c are in H.P., prove that (a)/(b+c), (b)/(c+a) and (c )/(a+b) are also in H.P.

If a+c = 2b and 2/c= 1/b+1/d then prove that a:b = c:d.

If a, b, c are in H.P., prove that, (a)/(b+c-a), (b)/(c+a-b), (c )/(a+b-c) are in H.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.

If a, b, c are in A.P., show that, (bc)/(a(b+c)), (ca)/(b(c+a)) and (ab)/(c(a+b)) are in H.P.

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. If the 20th term of a H.P. is 1 and the 30th  term is -1/17, then find...

    Text Solution

    |

  2. Find the sum 3/2-5/6+7/(18)-9/(54)+...oodot

    Text Solution

    |

  3. If a ,b ,ca n dd are in H.P., then prove that (b+c+d)//a ,(c+d+a)//b ,...

    Text Solution

    |

  4. The harmonic mean between two numbers is 21/5, their A.M. ' A ' and G....

    Text Solution

    |

  5. The mth term of a H.P is n and the nth term is m . Proves that its rth...

    Text Solution

    |

  6. The pth term of an A.P. is a and qth term is bdot Then find the sum o...

    Text Solution

    |

  7. If agt1,bgt1andcgt1 are in G.P., then show that 1/(1+log(e)a),1/(1+log...

    Text Solution

    |

  8. Solve the equation (x+1)+(x+4)+(x+7)+....+(x+28)=155.

    Text Solution

    |

  9. If a ,b ,a n dc be in G.P. and a+x ,b+x ,and c+x in H.P. then find the...

    Text Solution

    |

  10. The ratio of the sum of m and n terms of an A.P. is m^(2) :n^(2). Show...

    Text Solution

    |

  11. If first three terms of the sequence 1/16 ,a , b , 1/6 are in geometri...

    Text Solution

    |

  12. The sum of n ,2n ,3n terms of an A.P. are S1S2, S3, respectively. Prov...

    Text Solution

    |

  13. In a certain A.P., 5 times the 5th term is equal to 8 times the 8th ...

    Text Solution

    |

  14. If x is a positive real number different from 1, then prove that the n...

    Text Solution

    |

  15. Which term of the sequence 20 ,19 1/4, 18 1/2, 17 3/4,dot is the first...

    Text Solution

    |

  16. If Sn=n P+(n(n-1))/2Q ,w h e r eSn denotes the sum of the first n term...

    Text Solution

    |

  17. Find the sum sum(r=1)^n r(r+1)(r+2)(r+3)

    Text Solution

    |

  18. Find the sum sum(r=1)^n r/((r+1)!) where n!=1xx2xx3....n.

    Text Solution

    |

  19. Find the sum sum(r=1)^n r(r+1)(r+2)(r+3)

    Text Solution

    |

  20. Find the sum 1+1/(1+2)+1/(1+2+3)+..........+1/(1+2+3+.........+n)dot

    Text Solution

    |