Home
Class 12
MATHS
If the first 3 consecutive terms of a ge...

If the first 3 consecutive terms of a geometrical progression are the real roots of the equation `2x^3 - 19x^2 +57x - 54=0` find the sum to infinite number of terms of G.P.

Text Solution

Verified by Experts

`(27)/(2)`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -3 Subjective /JEE Advanced (Comprehension )|3 Videos

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -4 Level -I Previous Year /JEE Main|19 Videos

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -2 (Level -II) Multiple Correct /JEE Advanced|9 Videos

  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE 4 (PREVIOUS YEAR| JEE MAIN)|25 Videos

  • SOLUTION OF TRIANGLE

    MOTION|Exercise EXERCISE - 4( LEVEL II)|10 Videos

Similar Questions

Explore conceptually related problems

Find the number of real roots of the equation f(x) =x^(3) + 2x^(2) +x +2 =0

The number of real roots of the equation |x|^(2) -3|x| + 2 = 0 , is

If the first three terms of an A.P. are the roots of the equation 4x^(3) - 24x^(2) + 23 + 18 = 0 them compute the sum of the first n terms .

If 3x -4, x +4 and 5x +8 are the three positive consecutive terms of a geometric progression, then find the terms.

The sum of the terms of an infinite geometric progression is 3 and the sum of the squares of the terms is 81. Find the first term of the series.

The sum of the first 2012 terms of a geometric progression is 200. The sum of the first 4024 terms of the same series is 380. Find the sum of the first 6036 terms of the series.

Find the roots of the equation x^(4)+x^(3)-19x^(2)-49x-30 , given that the roots are all rational numbers.

MOTION-SEQUENCE & SERIES -Exercise -3 Subjective /JEE Advanced
  1. Find the sum in the nth group of sequence, (I 1,(2,3),(4,5,6,7),(8,9...

    Text Solution

    |

  2. Circles are inscribed in the acute angle alpha so that every neighbour...

    Text Solution

    |

  3. If the first 3 consecutive terms of a geometrical progression are the ...

    Text Solution

    |

  4. The sum of three numbers which are consecutive terms of an A.P. is 21....

    Text Solution

    |

  5. The sum of infinite number of terms of a G.P. is 4 and the sum of thei...

    Text Solution

    |

  6. Sum of the following series (i) 1+(2)/(2)+(3)/(2^2)+(4)/(2^3)+……..to...

    Text Solution

    |

  7. The sum of first ten terms of an A.P. is 155 and the sum of first two ...

    Text Solution

    |

  8. In a set of four number, the first three are in GP & the last three ar...

    Text Solution

    |

  9. Find the 4^(th) term of an H.P., whose 7^(th) term is 1/20 and 13^(th)...

    Text Solution

    |

  10. Find the sum of the n terms of the series whose nth term is (i) n(n+...

    Text Solution

    |

  11. Find the sum of the series (5)/(13)+(55)/(13)^2+(555)/(13)^2+(5555)/((...

    Text Solution

    |

  12. If the expression exp {1+|cosx|+cos^(3)x|+cos^(4)x+ . . . . oo)log(e...

    Text Solution

    |

  13. The sum of the infinite series , 1^2- 2^2 / 5+ 3^2 / 5^2 - 4^2 / 5^3 +...

    Text Solution

    |

  14. Find the sum of the n terms of the sequence 1/(1+1^2+1^4)+2/(1+2^2+2^...

    Text Solution

    |

  15. Find the sum of the first n terms ofthe sequence : 1+2(1+1/n)+3(1+1/n)...

    Text Solution

    |

  16. Find the n term and the sum to n terms of the sequence: (i) 1+5+13+29+...

    Text Solution

    |

  17. If sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2)+1/(3^2))+sqrt(1+1/(3^2)+1/(4...

    Text Solution

    |

  18. If a1,a,a3...an are in A.P then prove that a1^2-a2^2+a3^2-a4^2+....a(2...

    Text Solution

    |

  19. If a, b, c, d, e be 5 numbers such that a, b, c are in AP, b, c, d, ar...

    Text Solution

    |

  20. Using the relation A.M ge G.M. Prove that (i) tan theta +cot theta g...

    Text Solution

    |