Home
Class 11
MATHS
If Three number form an increasin G.P. I...

If Three number form an increasin G.P. If the
middle term is doubled , then the numbers are in
A.P. The common ratio of the G.P. is

A

`2-sqrt(3)`

B

`2+sqrt(3)`

C

`sqrt(2)+sqrt(3)`

D

`3+sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let the number be a,ar and `ar^(2)`, where `rgt1`. It is given that a, 2ar, `ar^(2)` are in AP.
`:." "4ar=a+ar^(2)rArrr^(2)-4r+1=0rArrr=2+sqrt(3)" "[becausergt1]`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|80 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos

  • SETS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

Three numbers form an increasing G.P. If the middle number is doubled, then the new numbers are in A.P. The common ratio of the G.P. is (A) 2-sqrt(3) (B) 2+sqrt(3) (C) sqrt(3)-2 (D) 3+sqrt(2)

Three positive numbers form an increasing GP. If the middle terms in this GP is doubled, the new numbers are in AP. Then, the common ratio of the GP is

Three positive numbers form an increasing GP. If the middle terms in this GP is doubled, the new numbers are in AP. Then, the common ratio of the GP is

If the pth ,qth and rth terms of an AP are in G.P then the common ration of the GP is

Three numbers are in G.P. If we double the middle term, we get an A.P. Then find the common ratio of the G.P.

If the 2nd , 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is :

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

If the pth, qth and rth terms of an A. P. are in G.P., prove that the common ratio of the G.P. is (q-r)/(p-q) .

In a G.P of positive terms if any term is equal to the sum of the next two terms, then the common ratio of the G.P is

In a G.P. of positive terms if any terms is equal to the sum of next tow terms, find the common ratio of the G.P.

OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Chapter Test
  1. If Three number form an increasin G.P. If the middle term is double...

    Text Solution

    |

  2. Let H(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n), then the sum to n terms...

    Text Solution

    |

  3. Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+............

    Text Solution

    |

  4. If A(1),A(2) are between two numbers, then (A(1)+A(2))/(H(1)+H(2)) is ...

    Text Solution

    |

  5. If the (m+1)t h ,(n+1)t h ,a n d(r+1)t h terms of an A.P., are in G.P....

    Text Solution

    |

  6. Given that n arithmetic means are inserted between two sets of numbers...

    Text Solution

    |

  7. If a,b, and c are in G.P then a+b,2b and b+ c are in

    Text Solution

    |

  8. If in a progression a1, a2, a3, e t cdot,(ar-a(r+1)) bears a constant...

    Text Solution

    |

  9. If in an AP, t1 = log10 a, t(n+1) = log10 b and t(2n+1) = log10 c then...

    Text Solution

    |

  10. Find the sum of the series: 1^2-2^2+3^2-4^2+.....-2008^2+2009^2.

    Text Solution

    |

  11. If 4a^(2)+9b^(2)+16c^(2)=2(3ab+6bc+4ca)," where "a,b,c are non-zero nu...

    Text Solution

    |

  12. If Sn denotes the sum of n terms of an A.P. whose common difference is...

    Text Solution

    |

  13. The sides of a right angled triangle are in A.P., then they are in the...

    Text Solution

    |

  14. Find the sum of all the 11 terms of an AP whose middle most term is 30...

    Text Solution

    |

  15. The maximum sum of the series 20+19 1/3+18 2/3+ is 310 b. 300 c. 0320 ...

    Text Solution

    |

  16. If three numbers are in G.P., then the numbers obtained by adding the ...

    Text Solution

    |

  17. If p ,q ,r are in A.P., show that the pth, qth and rth terms of any G....

    Text Solution

    |

  18. Let a,b,c be three positive prime number. The progrrssion in which sqr...

    Text Solution

    |

  19. If 1/(b-a)+1/(b-c)=1/a+1/c , then (A). a ,b ,a n dc are in H.P. (B). a...

    Text Solution

    |

  20. If three numbers are in H.P., then the numbers obtained by subtracting...

    Text Solution

    |

  21. The first three of four given numbers are in G.P. and their last three...

    Text Solution

    |