Home
Class 12
MATHS
A positive number is such that its fract...

A positive number is such that its fractional part, its integral part and the number itself constitute the first three terms of a geometrical progression. Show that the `n^(th)` term and the sum of the first n terms of the G.P. are, `2^n-2. cos^(n-2) (pi/5) and 2^n. cos^n (pi/5) -1` respectively.

Promotional Banner

Topper's Solved these Questions

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -1 Objective Problems /JEE Main Section -A : AP|24 Videos

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -2 (Level -I) Objective Problems /JEE Main AP|23 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

What is the product of first 2n+1 terms of a geometric progression ?

If the n^(th) term of an A.P.is (2n+1), find the sum of first n terms of the A.P.

If the n^(th) term of an A.P is (5n-2) ,find its first term

If the n^(th) term of an AP be (2n-1) then the sum of its first n terms will be

The sum of the first n terms of an A.P.is 3n+n^(2) find "(1)" the first term "(2)" and the sum of the first two terms

. The sum of the first three terms of an increesing G.P. is 21 and the sum of their squares is 189. Then the sum of its first n terms is

. The sum of the first three terms of an increasing G.P. is 21 and the sum of the their squaresis 189. Then sum of its first n terms is

The sum of the first three terms of an increasing G.P. is 21 and the sum of their squares is 189. Then the sum of its first n terms is

MOTION-SEQUENCE & SERIES -Exercise -4 Level -II Previous Year /JEE Advanced
  1. A positive number is such that its fractional part, its integral part ...

    Text Solution

    |

  2. Let Vr denote the sum of first r terms of an arithmetic progression (A...

    Text Solution

    |

  3. Let Vr denote the sum of the first r terms of an arithmetic progressio...

    Text Solution

    |

  4. Let Vr denote the sum of the first r terms of an arithmetic progressio...

    Text Solution

    |

  5. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

    Text Solution

    |

  6. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

    Text Solution

    |

  7. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

    Text Solution

    |

  8. A straight line through the vertex P of a triangle PQR intersects the ...

    Text Solution

    |

  9. Suppose four distinct positive numbers a1,a2,a3,a4 are in G.P. Let b1=...

    Text Solution

    |

  10. In the sum of first n terms of an A.P. is cn^2, then the sum of square...

    Text Solution

    |

  11. Let Sk ,k=1,2, ,100 , denotes thesum of the infinite geometric series ...

    Text Solution

    |

  12. Let a(1),a(2),a(3),"........."a(11) be real numbers satisfying a(1)=15...

    Text Solution

    |

  13. The minimum value of the sum of real number a^(-5),a^(-4),3a^(-3),1,a^...

    Text Solution

    |

  14. Let a1, a2, a3, ,a(100) be an arithmetic progression with a1=3a n dsp...

    Text Solution

    |

  15. If a(1),a(2),a(3),"......" be in harmonic progression with a(1)=5 and ...

    Text Solution

    |

  16. Let a(n) denote the number of all n-digit numbers formed by the digits...

    Text Solution

    |

  17. Let an denote the number of all n-digit positive integers formed by th...

    Text Solution

    |

  18. Let S(n)=sum(k=1)^(4n)(-1)^((k(k+1))/2)k^(2). Then S(n) can take value...

    Text Solution

    |

  19. A pack contains n cards numbered from 1 to n. Two consecutive numbered...

    Text Solution

    |

  20. Let a,b,c be positive integers such that (b)/(a) is an integer. If a,b...

    Text Solution

    |

  21. Suppose that all the terms of an arithmetic progression (A.P.) are nat...

    Text Solution

    |