Home
Class 12
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.

Text Solution

Verified by Experts

a,b,c, and d are in H.P.
`rArr1/a,1/b,1/c,1/d` are in A.P.
`rArr(a+b+c+d)/a,(a+b+c+d)/b,(a+b+c+d)/c,(a+b+c+d)/d` are in A.P.
`rArr1+(b+c+d)/a,(a+c+d)/b+1,(a+b+d)/c+1,(a+b+c)/d+1` are in A.P.
`rArr (b+c+d)/a,(a+c+d)/b,(a+b+d)/c,(a+b+c)/d` are in A.P.
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.1|3 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.2|10 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Multiple Correct Answer|4 Videos

  • PROBABILITY II

    CENGAGE|Exercise JEE Advanced Previous Year|25 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

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, b, c, d are in G.P., then (a + b + c + d)^(2) is equal to

If a ,b ,c are in A.P., then prove that the following are also in A.P. a^2(b+c),b^2(c+a),c^2(a+b)

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

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

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 ,d ,e are in A.P., the find the value of a-4b+6c-4d+edot

If a ,b ,c are in A.P., then prove that the following are also in A.P. a(1/b+1/c),b(1/c+1/a),c(1/a+1/b)

If a,b,c are in A.P. then (a-b)/(b-c) is equal to ………….

If (b+c-a)/a ,(c+a-b)/b ,(a+b-c)/c , are in A.P., prove that 1/a ,1/b ,1/c are also in A.P.

CENGAGE-PROGRESSION AND SERIES-Examples
  1. If the 20th term of a H.P. is 1 and the 30th term is -1/17, then find ...

    Text Solution

    |

  2. If (a-x)/(p x)=(a-y)/(q y)=(a-z)/ra n dp ,q ,a n dr are in A.P., then ...

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

    Text Solution

    |

  5. If a >1,b >1a n dc >1 are in G.P. then show that 1/(1+(log)e a),1/(1+(...

    Text Solution

    |

  6. If a ,b ,a n dc be in G.P. and a+x ,b+x ,a n dc+x in H.P. then find th...

    Text Solution

    |

  7. If first three terms of the sequence 1//16 ,a , b , c1//16 are in geom...

    Text Solution

    |

  8. if (m+1)th, (n+1)th and (r+1)th term of an AP are in GP.and m, n and r...

    Text Solution

    |

  9. Insert four H.M.s between 2/3 and 2/13.

    Text Solution

    |

  10. If nine arithmetic means and nine harmonic means are inserted between ...

    Text Solution

    |

  11. Let a ,b be positive real numbers. If a A1, A2, b be are in arithmetic...

    Text Solution

    |

  12. The A.M. and H.M. between two numbers are 27 and 12, respectively, t...

    Text Solution

    |

  13. If the A.M. between two numbers exceeds their G.M. by 2 and the GM. ...

    Text Solution

    |

  14. Find the sum 2017+1/4(2016+1/4(2015+…+1/4(2+1/4(1))..))

    Text Solution

    |

  15. The sum of 50 terms of the series 1+2(1+1/(50))+3(1+1/(50))^2+ is give...

    Text Solution

    |

  16. Find the sum to ininity of the series 1-3x+5x^2+7x^3+..... oo when Ix|...

    Text Solution

    |

  17. The sum of the infinite series 1+(1+1/5)(1/2)+(1+1/5+1/(5^2))(1/(2^2))...

    Text Solution

    |

  18. If the sum to infinity of the series 3+(3+d)1/4+(3+2d)1/(4^2)+oo is (4...

    Text Solution

    |

  19. Find the sum to infinity of the series 1^2+2^2+3^2+4^2+oodot

    Text Solution

    |

  20. Find the sum 2xx5+5xx9+8xx13+11xx17+.. n terms.

    Text Solution

    |