Home
Class 10
MATHS
If the p^(t h),q^(t h)and r^(t h)terms ...

If the `p^(t h)`,`q^(t h)`and `r^(t h)`terms of a GP are a, b and c, respectively. Prove that `a^(q-r)b^(r-p)c^(p-q)=1`.

Text Solution

Verified by Experts

The correct Answer is:
`A^(@)*R^(@)=1`
Promotional Banner

Topper's Solved these Questions

  • GEOMETRIC PROGRESSION

    ICSE|Exercise Exercise 11(A) |14 Videos

  • GEOMETRIC PROGRESSION

    ICSE|Exercise Exercise 11(B) |10 Videos

  • FACTORISATION

    ICSE|Exercise M.C.Q(Competency Based Questions )|15 Videos

  • GOODS AND SERVICE TEX (GST)

    ICSE|Exercise Competency Based Questions |20 Videos

Similar Questions

Explore conceptually related problems

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

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 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

The 5^(t h) , 8^(t h) and 11^(t h) terms of a G.P. are p, q and s, respectively. Show that q^2=p s .

If the p t h ,\ q t h\ a n d\ r t h terms of a G.P. are a ,\ b ,\ c respectively, prove that: a^((q-r))dot^b^((r-p))dotc^((p-q))=1.

If pth,qth and rth terms of an A.P. are a, b, c respectively, then show that (i) a(q-r)+b(r-p)+c(p-q)=0

If p^(t h),\ q^(t h),\ a n d\ r^(t h) terms of an A.P. and G.P. are both a ,\ b\ a n d\ c respectively show that a^(b-c)b^(c-a)c^(a-b)=1.

If the p^(t h) and q^(t h) terms of a G.P. are q and p respectively, show that (p+q)^(t h) term is ((q^p)/(p^q))^(1/(p-q)) .

If the p^(t h)a n d q^(t h) terms of a G.P. are q a n d p respectively, show that (p+q)^(t h) term is ((q^p)/(p^q))^(1/(p-q)) .

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

ICSE-GEOMETRIC PROGRESSION -Exercise 11(D)
  1. If the p^(t h),q^(t h)and r^(t h)terms of a GP are a, b and c, respec...

    Text Solution

    |

  2. Find the sum of G.P. : 1+3+9+27+ . . . . .. . to 12 terms.

    Text Solution

    |

  3. Find the sum of G.P. : 0*3+0*03+0*003+0*0003+ . . . . . . . to 8 ter...

    Text Solution

    |

  4. Find the sum of G.P. : 1-(1)/(2)+(1)/(4)-(1)/(8)+ . . . .. . . .. . ...

    Text Solution

    |

  5. Find the sum of G.P. : 1-(1)/(3)+(1)/(3^(2))-(1)/(3^(3))+ . . . .. ....

    Text Solution

    |

  6. Find the sum of G.P. : (x+y)/(x-y)+1+(x-y)/(x+y)+ . . . . .. . . . ...

    Text Solution

    |

  7. Find the sum of G.P. : sqrt(3)+(1)/(sqrt(3))+(1)/(3sqrt(3))+ . . . ....

    Text Solution

    |

  8. How many terms of the geometric progression 1+4+16+64+ . . . . .. . . ...

    Text Solution

    |

  9. If the first term of a G.P is 27 and 8th term is 1/81, then the sum of...

    Text Solution

    |

  10. A boy spends Rs. 10 on first day, Rs. 20 on second day, Rs. 40 on thir...

    Text Solution

    |

  11. The 4^(th) and the 7^(th) terms of a G.P. are (1)/(27) and (1)/(729) r...

    Text Solution

    |

  12. A geometric progression has common ratio = 3 and last term = 486. If t...

    Text Solution

    |

  13. Find the sum of G.P. : 3,6,12, . . . . . . . . ., 1536.

    Text Solution

    |

  14. How many terms of the series 2+6+18+ . . . . . . . . . . . Must be tak...

    Text Solution

    |

  15. In a G.P., the ratio between the sum of first three terms and that of ...

    Text Solution

    |

  16. How many terms of the G.P. (2)/(9),-(1)/(3),(1)/(2), . . . . . . . ....

    Text Solution

    |

  17. If the sum of 1+2+2^(2)+ . . . . . . . . . .+2^(n-1) is 255, find the ...

    Text Solution

    |

  18. Find the geometric mean between : (4)/(9) and (9)/(4)

    Text Solution

    |

  19. Find the geometric mean between : 14 and (7)/(32)

    Text Solution

    |

  20. Find the geometric mean between : 2a and 8a^(3)

    Text Solution

    |

  21. The sum of three numbers in G.P. is (39)/(10) and their product is 1. ...

    Text Solution

    |