Home
Class 12
MATHS
The sum of an infinite geometric series ...

The sum of an infinite geometric series with positive terms is 3 and the sums of the cubes of its terms is `(27)/(19)`. Then the common ratio of this series is

A

`(4)/(9)`

B

`(2)/(9)`

C

`(2)/(3)`

D

`(1)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is (27)/(19) . Then, the common ratio of this series is

In a geometric progression consisting of positive terms each term equals the sum of the next two terms. Then the common ratio of this progression equals

In a geometric progression consisting of positive terms, each term equals the sum of the next terms. Then find the common ratio.

The sum of an infinite geometric series is 162 and the sum of its first n terms is 160. If the inverse of its common ratio is an integer, then which of the following is not a possible first term? 108 b. 144 c. 160 d. none of these

The first term of an infinite geometric series is 21. The second term and the sum of the series are both positive integers. Then which of the following is not the possible value of the second term 12 b. 14 c. 18 d. none of these

The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, then the common ratio of the G.P. is

In an infinite geometric series the first term is a and common ratio is r . If the sum of the series is 4 and the seond term is 3/4 , then (a, r) is

consider an infinite geometric series with first term a and comman ratio r if the sum is 4 and the second term is 3/4 then find a&r

The sum of an infinite G.P. is 18. if the first term is 6, the common ratio is

CENGAGE-JEE 2019-MCQ
  1. The sum of all two digit positive numbers which when divided by 7 yiel...

    Text Solution

    |

  2. If 5, 5r and 5r^(2) are the lengths of the sides of a triangle, then r...

    Text Solution

    |

  3. The sum of an infinite geometric series with positive terms is 3 and t...

    Text Solution

    |

  4. Let a1, a2, a3, ?a10 are in G.P. if a3/a1 =25 then a9/a5 is equal to ...

    Text Solution

    |

  5. If 19th term of a non-zero AP is zero, then its (49th term) : (29 th t...

    Text Solution

    |

  6. The product of three consecutive terms of a GP is 512. If 4 is added t...

    Text Solution

    |

  7. Let S(k) = (1+2+3+...+k)/(k). If S(1)^(2) + s(2)^(2) +...+S(10)^(2) = ...

    Text Solution

    |

  8. If the sum of the first 15 terms of the series ((3)/(4))^(3)+(1(1)/(2)...

    Text Solution

    |

  9. Let x, y be positive real numbers and m, n be positive integers, The ...

    Text Solution

    |

  10. Consider a class of 5 girls and 7 boys. The number of different teams ...

    Text Solution

    |

  11. Let S be the set of all triangles in the xy-plane, each having one ver...

    Text Solution

    |

  12. The number of natural numbers less than 7,000 which can be formed by u...

    Text Solution

    |

  13. If set A={1, 2, 3, 2 }, then the find the number of onto functions fro...

    Text Solution

    |

  14. Let S={1,2,3, …, 100}. The number of non-empty subsets A to S such tha...

    Text Solution

    |

  15. Consider three boxes, each containing 10 balls labelled 1, 2, …, 10. S...

    Text Solution

    |

  16. Let Z be the set of integers. If A = {x in Z : 2^((x + 2)(x^(2) - 5x +...

    Text Solution

    |

  17. There are m men and two women participating in a chess tournament. Eac...

    Text Solution

    |

  18. If the fractional part of the number (2^(403))/(15) is (k)/(15) then k...

    Text Solution

    |

  19. The coefficient of t^4 in ((1-t^6)/(1-t))^3 (a) 18 (b) 12 ...

    Text Solution

    |

  20. If Sigma(i=1)^(20) ((""^(20)C(i-1))/(""^(20)C(i)+""^(20)C(i-1)))^(3)=(...

    Text Solution

    |