Home
Class 11
MATHS
If a(1/b+1/c), b(1/c+1/a), c(1/a+1/b) ar...

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

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If a, b, c are in A.P., prove that : b+c,c+a,a+ b are also in A.P.

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

If a+b+c ne 0 and (b + c)/a, (c + a)/b, (a + b)/c are in A.P., prove that : 1/a,1/b,1/c are also in A.P.

If a^2 (b+c),b^2(c+a) , c^2(a+b) are in A.P., show that : either a, b, c are in A.P. or ab + bc + ca =0.

If a ((1)/(b) + (1)/(c)) , b((1)/(c) + (1)/(a)) , c ((1)/(a)+ (1)/(b)) are in AP then a, b, c are in :

If a,b,c are in A.P. then :

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 are in A.P. then 3^a, 3^b, 3^c are in:

If a, b, c are in A.P., prove that : (bc)^-1,(ca)^-1 and (ab)^-1 are also in A.P.

If 1/a+1/(a-b)+1/c+1/(c-b)= 0 and a + c-b!=0 , then prove that a, b, c are in H.P.

PSEB-SEQUENCES AND SERIES-EXERCISE
  1. If (a+bx)/(a-bx)=(b +cx)/(b-cx)=(c+dx)/(c-dx) (x ne 0), then show that...

    Text Solution

    |

  2. Let S be the sum, P the product and R the sum of reciprocals of n term...

    Text Solution

    |

  3. The p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c, respective...

    Text Solution

    |

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

    Text Solution

    |

  5. If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n + ...

    Text Solution

    |

  6. If a and b are the roots of x^2 -3x + p= 0 and c, d are roots of x^2 -...

    Text Solution

    |

  7. The ratio of the A.M. and G.M. of two positive numbers a and b, is m :...

    Text Solution

    |

  8. 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....

    Text Solution

    |

  9. Find the sum of the following series up to n terms: .6+. 66 +. 666+...

    Text Solution

    |

  10. Find the 20th term of the series 2xx4 + 4xx6 + 6xx8 +...+n terms.

    Text Solution

    |

  11. Find the sum of the first n terms of the series: 3+7+13 +21 +31 +...

    Text Solution

    |

  12. If S1,S2, S3 are the sum of first n natural numbers, their squares and...

    Text Solution

    |

  13. Find the sum of the following series up to n terms: 1^3/1+(1^3+2^3)/(1...

    Text Solution

    |

  14. Show that (1xx2^2+2xx3^2+....+nxx(n+1)^2)/(1^2xx2+2^2xx3+...+n^2xx(n+1...

    Text Solution

    |

  15. A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and ag...

    Text Solution

    |

  16. Shamshad Ali buys a scooterfor Rs 22000. He pays Rs 4000 cash and agre...

    Text Solution

    |

  17. A person writes a letter to four of his friends. He asks each one of t...

    Text Solution

    |

  18. Aman deposited Rs 10000 in a bank at the rate of 5% simple interest an...

    Text Solution

    |

  19. A manufacturer reckons that the value of a machine, which costs him Rs...

    Text Solution

    |

  20. 150 workers were engaged to finish a job in a certain number of days. ...

    Text Solution

    |