Home
Class 12
MATHS
The first term of a GP is unity. For wha...

The first term of a GP is unity. For what value of the common ratio of the progression the sum of 4 times the second term and 5 times the third term will be minimum ?

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • Product of two Vectors

    A DAS GUPTA|Exercise Exercise|48 Videos

  • Properties and Application of definite Integrals

    A DAS GUPTA|Exercise EXERCISE|62 Videos

Similar Questions

Explore conceptually related problems

If the first term of the G.P is unity,and value of 4a_(2)+5a_(3) is minimum then find the sum to infinite terms

The first term of a GP is 1 and the sum of its 3rd and 5th terms is 90. Find the common ratio of the GP.

The sum of an infinite GP whose common ratio is numerically less than 1 is 32 and the sum of the first two terms is 24. What will be the third term ?

The sum of first 6 terms of a G.P. is nine times the sum of the first 3 terms. Find the common ratio.

The sum of first 12 terms of a G.P. is five times the sum of the first 6 terms. Find the common ratio.

The first term of a G.P.is 1. The sum of the third and fifth terms is 90. Find the common ratio of the G.P.

A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
  1. The product of three numbers in GP is 216 and their sum is 19. Find th...

    Text Solution

    |

  2. Divide 63 into three parts that are in GP and the product of the first...

    Text Solution

    |

  3. The first term of a GP is unity. For what value of the common ratio of...

    Text Solution

    |

  4. For the series sum t(n,) Sn=sum(n=1)^ntn=2tn-1. Is the series geometri...

    Text Solution

    |

  5. If S1, S2, S3 are the sums to n, 2n, 3n terms respectively for a GP th...

    Text Solution

    |

  6. If S1, S2, S3 be respectively the sums of n ,2n ,3n terms of a G.P., t...

    Text Solution

    |

  7. Find sum(n=1)^n un if un=sum(n=0)^n1/2^n.

    Text Solution

    |

  8. STATEMENT -1: (666...n digit)^2+(888... ndigit)=(444....2ndigits) STAT...

    Text Solution

    |

  9. Let a1,a2,a3,.... are in GP. If an>am when n>m and a1+an=66 while a2*a...

    Text Solution

    |

  10. Find the sum of 2n terms of the series whose every even term is ' a ' ...

    Text Solution

    |

  11. If the sum of an infinite G.P is 32 and the some of its first two term...

    Text Solution

    |

  12. If Sn=1+r^n+r^(2n)+r^(3n)+.... to oo and sn=1-r^n+r^(2n)-r^(3n)+... to...

    Text Solution

    |

  13. If x=sum(n=0)^oo a^n, y=sum(n=0)^oo b^n where |a|<1,|b|<1 then prove t...

    Text Solution

    |

  14. If exp. {(sin^2x+sin^4x+sin^6x+…inf.) In2} satisfies the equation x^2-...

    Text Solution

    |

  15. If S1, S2,S3,S4,.....,Sp denotes the sums of infinite geometric serie...

    Text Solution

    |

  16. If S1, S2,S3,S4,.....,Sp denotes the sums of infinite geometric serie...

    Text Solution

    |

  17. If S1, S2,S3,S4,.....,Sp denotes the sums of infinite geometric serie...

    Text Solution

    |

  18. If a,b,c are in G.P., then show that : loga, logb, log c are in A.P.

    Text Solution

    |

  19. If a,b,c are in A.P. and x,y,z in G.P., prove that x^(b-c).y^(c-a).z^(...

    Text Solution

    |

  20. If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d ...

    Text Solution

    |