Home
Class 12
MATHS
The sum of the first three terms of a G....

The sum of the first three terms of a G.P. is 16 and the sum of the next three terms is 128.
(i) Determine the first term and common ratio.
(ii) Find also the sum of `n` terms of the G.P.

Text Solution

Verified by Experts

The correct Answer is:
(i) `a = 16/7` (ii) `16/7 (2^(n) - 1)`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|49 Videos

  • SEQUENCES AND SERIES

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|105 Videos

  • RELATIONS AND FUNCTIONS

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|33 Videos

  • SETS

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|21 Videos

Similar Questions

Explore conceptually related problems

the sum of the first n terms of a sequence is an^(2) + bn . Then the sum of the next n terms is

the sum of the first six terms of a GP is 9 times the sum of the first three terms. The common ratio is

The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.

The sum of first three terms of a G.P. is and their product is 1. Find the common ratio and the terms.

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

Find the sum of 7 terms of the G.P. 1,-3,9,-27....

Find the sum of the first 30 terms of an A.P. whose nth term is 3 + 2n.

NEW JOYTHI PUBLICATION-SEQUENCES AND SERIES -QUESTIONS FROM COMPETITIVE EXAMS
  1. The sum of the first three terms of a G.P. is 16 and the sum of the ne...

    Text Solution

    |

  2. The sum to n terms of the series 1/2 + 3/4 + 7/8 + 15/16 + ....... is

    Text Solution

    |

  3. 0.2 + 0.22 + 0.222 + …….. to n terms =

    Text Solution

    |

  4. If (a^(n + 1) + b^(n + 1))/(a^(n) + b^(n)) is the arithmetic mean betw...

    Text Solution

    |

  5. If (i)^(2) = -1, (i)^(2) + (i)^(4) + (i)^(6) + ...... to (2n + 1) term...

    Text Solution

    |

  6. If S(n) denotes the sum of n terms of an A.P., S(n +3) - 3S(n + 2) + 3...

    Text Solution

    |

  7. The HM of 2 numbers is 4. Their AM is A and GM is G. If G satisfies 2...

    Text Solution

    |

  8. The angle of triangle are in 30^(@). The greatest angle in radians is

    Text Solution

    |

  9. How many terms of the geometric series 1 + 4 + 16 + 64 + ……… will make...

    Text Solution

    |

  10. Find the value of n so that (a^(n+1)+b^(n+1))/(a^(n)+b^n) may be the ...

    Text Solution

    |

  11. The sum of the series 1 + 2.2 + 3.2^(2) + 4.2^(3) + 5.2^(4) + ……… + 1...

    Text Solution

    |

  12. If A, G, H denote respectively the AM, GM and HM between two unequal p...

    Text Solution

    |

  13. Let a, b, c be district real numbers. If a, b, c are in G.P and a + b ...

    Text Solution

    |

  14. The numbers of terms of the A.P 3, 7, 11, 15, …… to be taken so that t...

    Text Solution

    |

  15. If the progression 3, 10, 17, …… and 63, 65, 67, …… are such that thei...

    Text Solution

    |

  16. Which term of the geometric sequence 5,2,4/5 , 8/(25) … is (128)/(15...

    Text Solution

    |

  17. If a, b and c are respectively the p^(th),q^(th)and r^(th) terms of an...

    Text Solution

    |

  18. The sum of infinite terms of the geometric progression (sqrt(2) + 1)/(...

    Text Solution

    |

  19. The two geometric means between the numbers 1 and 64 are

    Text Solution

    |

  20. If 1 + (1 + 2)/2 + (1 + 2 + 3)/3 + ...... to n terms is s, then s is e...

    Text Solution

    |

  21. If a, b, and c are in A.P., then which one of thew following is not tr...

    Text Solution

    |