Home
Class 12
MATHS
If S1, S2, S3 are the sums to n, 2n, 3n ...

If `S_1, S_2, S_3` are the sums to n, 2n, 3n terms respectively for a GP then prove that `S_1,S_2-S_1,S_3-S_2` are in GP.

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 S_(1), S_(2), S_(3) are the sums of n, 2n, 3n terms respectively of an A.P., then S_(3)//(S_(2) - S_(1))-

If S_(1),S_(2),S_(3) be respectively the sums of n,2n,3n terms of a G.P.,then prove that S_(1)^(2)+S_(2)^(2)=S_(1)(S_(2)+S_(3))

If S_1 ,S_2 and S_3 denote the sum of first n_1,n_2 and n_3 terms respectively of an A.P. Then S_1/n_1 (n_2-n_3) + S_2/n_2 (n_3-n_1)+S_3/n_3 (n_1-n_2) equals :

If S_(1),S_(2),S_(3) be respectively the sums of n,2n and 3n terms of a G.P.,prove that S_(1)(S_(3)-S_(2))=(S_(2)-S_(1))^(2)

If s_(1),s_(2)and s_(3) are the sum of first n , 2n, 3n terms respectively of an arithmetical progression , then show that s_(3)=3 (s_(2)-s_(1))

If S_(1),S_(2) andS _(3) be respectively the sum of n,2n and 3n terms of a G.P.prove that S_(1)(S_(3)-S_(2))=(S_(2)-S_(1))^(2)

If S_(n) denotes the sum of n terms of a G.P., prove that: (S_(10)-S_(20))^(2)=S_(10)(S_(30)-S_(20))

A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
  1. The first term of a GP is unity. For what value of the common ratio of...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. 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

    |

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

    Text Solution

    |

  19. 29. If a,b,c are in G.P. and a^(1/x)=b^(1/y)=c^(1/z) prove that x, y, ...

    Text Solution

    |

  20. If a, x, b as well as c, x, d are in GP while a^2,y,b^2 as well as c^2...

    Text Solution

    |