Home
Class 11
MATHS
If p, q, r are in A.P. while x, y, z are...

If p, q, r are in A.P. while x, y, z are in G.P., prove that `x^(q-r).y^(r-p).z^(p-q) =1`.

A

1

B

`x+y+z`

C

xyz

D

`p+q+r`.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise EXERCISE|435 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE|226 Videos

  • SETS

    MODERN PUBLICATION|Exercise EXERCISE|381 Videos

Similar Questions

Explore conceptually related problems

If a,b,c are in A.P. and x,y,z are in G.P., then show that x^(b-c).y(c-a).z(a-b)=1 .

If the pth , qth , rth , terms of a GP . Are x,y,z respectively prove that : x^(q-r).y^(r-p).z^(p-q)=1

If the pth, qth and rth terms of an A.P. be x,y,z repsectively, then show that : x(q-r)+y(r-p)+z(p-q)=0

If the p^(th) , q^(th) and r^(th) terms of a G.P. are a, b and c, respectively. Prove that a^(q-r) b^(r-p)c^(P-q)=1 .

Sum of the first p, q and r terms of an A.P. are a, b and c, respectively. Prove that a/p(q-r)+b/q(r-p)+c/r(p-q)=0

Sum of first p,q and r terms of an A.P. are a,b,c respectively. Prove that a/p(q-r) +b/q(r-p) + c/r(p-q)=0 .

If x, 2y, 3z are in A.P where distinct numbers x,y,z are in GP then the common ratio of the G.P. is

If p ,q, r are in A.P., a is G.M. between p, q and b is G.M. between q, r, then prove that a^2, q^2, b^2 are in A.P.

The p^(th) , q^(th) and r^(th) terms of an A.P. are a, b, c, respectively. Show that (q -r)a+ (r-p )b + (p- q)c= 0

If agt0,bgt0,cgt0 be respectively the pth, qth and rth terms of a G.P. are a, b ,c , prove that : (q-r) log a+ (r -p) log b + (p -q) log c = 0 .

MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. If the sum of n natural numbers is one sixth of their squares, then n ...

    Text Solution

    |

  2. The sum of the numbers 1, 4, 9, 16, ... , 100 is :

    Text Solution

    |

  3. If p, q, r are in A.P. while x, y, z are in G.P., prove that x^(q-r).y...

    Text Solution

    |

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

    Text Solution

    |

  5. If a,b,c are in AP and (a+2b-c)(2b+c-a)(c+a-b)=lambdaabc, then lambda...

    Text Solution

    |

  6. If (a^n+b^n)/(a^(n-1)+b^(n-1)) is the A.M. between a and b, then find ...

    Text Solution

    |

  7. Sum of the series 1^(2) + 3^(2) + 5^(2) + … + n^(2) is :

    Text Solution

    |

  8. 11^3+12^3+13^3+....+20^3 is :

    Text Solution

    |

  9. If the 10th term of a G.P. is 9 and 4th term is 4, then its 7th term i...

    Text Solution

    |

  10. The 6th term of a G.P. is 32 and its 8th term is 128, then the value o...

    Text Solution

    |

  11. 11^3+12^3+13^3+....+20^3 is :

    Text Solution

    |

  12. A boy goes to school from his home at a speed of x km/hr. and comes ba...

    Text Solution

    |

  13. If a,a(1),a(2),a(3),"......",a(2n)b are in AP and a,b(1),b(2),b(3),".....

    Text Solution

    |

  14. The sum of the products of the ten numbers pm1,pm2,pm3,pm4,pm5 takung ...

    Text Solution

    |

  15. Find the value of the expression sum(i=1)^(n)sum(j=1)^(i)sum(k=1)^(j)1...

    Text Solution

    |

  16. If x is a positive number different from 1, such that logax,logbx and ...

    Text Solution

    |

  17. For what value of m, (a^(m+1)+b^(m+1))/(a^m+b^m) is the arithmetic mea...

    Text Solution

    |

  18. If a, b, c are in G.P. and x, y are arithmetic mean of a, b and b, c r...

    Text Solution

    |

  19. A student read common difference of an A.P. as -3 instead of 3 and obt...

    Text Solution

    |

  20. If a1=1 and an =na(n-1), for all positive integers n ge 2, then a5 is ...

    Text Solution

    |