Home
Class 12
MATHS
if x , 2y and 3z are in AP where the d...

if x , 2y and 3z are in AP where the distinct numbers x, yand z are in gp. Then the common ratio of the GP is

A

3

B

`1/3`

C

2

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
B
x,y and z are in G.P. Hence,
`y=xr,=xr^(2)`
Also,x,2y, and 3z are in A.P. Hnce,
4y=x+3z
`rArr4xr=x+3xr^(2)`
`rArr3r^(2)-4r+1=0`
`rArr(3r-1)(r-1)=0`
`rArrr=1//3` (rne1 is not possible as x,y,z are distinct)
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise EXERCIESE ( MULTIPLE CORRECT ANSWER TYPE )|1 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise (Multiple & Comprehension)|65 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.9|9 Videos

  • PROBABILITY II

    CENGAGE|Exercise NUMARICAL VALUE TYPE|2 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

If x,2y,z are in AP where the distinct numbers x,y,z are in GP.Then the common ratio of the GP is (A) 3 (B) (1)/(3)(C)2(D)(1)/(2)

If the pth,qth & rth terms of an AP are in GP. Find the common ratio of the GP.

Three positive numbers form an increasing GP. If the middle term in this GP is doubled, then 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 x,2y,3z are in A.P. where x,y,z are unequal number in a G.P., then the common ratio of this G.P. is (a) 3 (b) 1/3 (c) 2 (d) 1/2

The pth, (2p)th and (4p)th terms of an AP, are in GP, then find the common ratio of GP.

Three distinct numbers a, b, c form a GP in that order and the numbers a+b, b+c, c+a form an AP in that order. Then the common ratio of the GP is

If the 2nd, 5th, and 9th terms of a non-euatant AP are in GP, then the common ratio of this GP is

CENGAGE-PROGRESSION AND SERIES-Exercise (Single)
  1. If a ,b, c ,d are in G.P, then (b-c)^2+(c-a)^2+(d-b)^2 is equal to

    Text Solution

    |

  2. Let {tn} be a sequence of integers in G.P. in which t4: t6=1:4a n dt2+...

    Text Solution

    |

  3. if x , 2y and 3z are in AP where the distinct numbers x, yand z ar...

    Text Solution

    |

  4. If a,b, and c are in A.P and b-a,c-b and a are in G.P then a:b:c is

    Text Solution

    |

  5. If the sides of a triangle are in G.P., and its largest angle is twice...

    Text Solution

    |

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

    Text Solution

    |

  7. The number of terms common between the series 1+ 2 + 4 + 8..... to 100...

    Text Solution

    |

  8. If a^2+b^2,a b+b c ,a n db^2+c^2 are in G.P., then a ,b ,c are in a. A...

    Text Solution

    |

  9. In a G.P. the first, third, and fifth terms may be considered as the ...

    Text Solution

    |

  10. If the pth ,qth and rth terms of an AP are in G.P then the common rati...

    Text Solution

    |

  11. If pth, qth , rth and sth terms of an AP are in GP then show that (p-q...

    Text Solution

    |

  12. If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmet...

    Text Solution

    |

  13. If a ,ba n dc are in A.P., and pa n dp ' are respectively, A.M. and G....

    Text Solution

    |

  14. If (1+x)(1+x^2)(1+x^4)….(1+x^(128))=Sigma(r=0)^(n) x^r, then n is equa...

    Text Solution

    |

  15. If (1-p)(1+3x+9x^2+27 x^3+81 x^4+243 x^5)=1-p^6p!=1 , then the value o...

    Text Solution

    |

  16. Consider the ten numbers a r ,a r^2, a r^3, ,a r^(10)dot If their sum...

    Text Solution

    |

  17. If x ,y ,a n dz are distinct prime numbers, then x , y , a n dz may be...

    Text Solution

    |

  18. Let a=111 1(55d igi t s),b=1+10+1=^2++10^4,c=1+10^5+10^(10)+10^(15)++1...

    Text Solution

    |

  19. Let an be the nth therm of a G.P of positive numbers .Let Sigma(n=1)^(...

    Text Solution

    |

  20. The sum of 20 terms of a series of which every term is 2 times the ter...

    Text Solution

    |