Home
Class 11
MATHS
Let the sum of n, 2n, 3n terms of an A.P...

Let the sum of n, 2n, 3n terms of an A.P. be `S_1`, `S_2` and `S_3`, respectively, show that `S_3 = 3(S_2 - S_1)`

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise EXERCISE|435 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE|226 Videos

  • SETS

    MODERN PUBLICATION|Exercise EXERCISE|381 Videos

Similar Questions

Explore conceptually related problems

The sum of n terms of an A.P. is 3n^2 + 4n . Find the A.P.

If S_1 , S_2 , S_3 are the sum of first n natural numbers, their squares and their cubes, respectively, show that 9 S_2^2=S_3(1+8S_1) .

If S_n represents the sum of n terms of a G.P. whose first term and common ratio are a and r respectively. Prove that : S_1 +S_2+S_3+.....+S_(m)= (am)/(1-r)-(ar(1-r^(m)))/((1-r)^2) .

If the sum of n terms of an A.P. is 3n^2 + 2n : Find the rth term.

If S_n denotes the sum of n terms of a G.P. whose first term and common ratio are a and r respectively, then : S_1 +S_3+S_5+.....+S_(2n-1)= (an)/(1-r)-(ar(1-r^(2n)))/((1-r)^2 (1+r)) .

Let S_n denote the sum of first n terms of an AP and 3S_n=S_(2n) What is S_(3n):S_n equal to? What is S_(3n):S_(2n) equal to?

If S_1,S_2,S_3 be the sum of n, 2n, 3n terms of a G.P., show that : S_1(S_3-S_2)= (S_2-S_1)^2 .

If S_(1),S_(2),S_(3) be respectively the sum of n, 2n and 3n terms of a GP, then (S_(1)(S_(3)-S_(2)))/((S_(2)-S_(1))^(2)) is equal to

In an A.P., S_(3)=6 and S_(6)=3 prove that: 2(2n+1)S_(n+4)=(n+4)S_(2n+1) .

MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. If in an A.P. S1=6 and S7=105, prove that : S(n),S(n-3)::(n+3),(n-3)...

    Text Solution

    |

  2. In an A.P., S(3)=6 and S(6)=3 prove that: 2(2n+1)S(n+4)=(n+4)S(2n+1)...

    Text Solution

    |

  3. Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respective...

    Text Solution

    |

  4. If ‘a’ and ‘b’ are respectively the pth and qth terms of an A.P., show...

    Text Solution

    |

  5. Sum of first p,q and r terms of an A.P. are a,b,c respectively. Prove...

    Text Solution

    |

  6. Find the A.M. between : 3.7 and 5.5.

    Text Solution

    |

  7. Find the A.M. between : 6 and -8.

    Text Solution

    |

  8. Insert 3 arithmetic means between : 3 and 15.

    Text Solution

    |

  9. Insert 3 arithmetic means between : 5 and 21.

    Text Solution

    |

  10. Insert 5 arithmetic means between 8 and 26.

    Text Solution

    |

  11. Insert 6 arithmetic means between 3 and 24.

    Text Solution

    |

  12. Insert 10 arithmetic means between 2 and 57.

    Text Solution

    |

  13. If A is the A.M. between a and b, prove that : (A-a)^(2) +(A-b)^(2)=...

    Text Solution

    |

  14. If A is the A.M. between a and b, prove that : 4(a-A)(A-b)=(a-b)^(2...

    Text Solution

    |

  15. If A1 and A2 are two A.M.’s between a and b, prove that : (2A1-A2)(2...

    Text Solution

    |

  16. If A1 and A2 are two A.M.’s between a and b, prove that : A1+A2 =a+b...

    Text Solution

    |

  17. Insert 10 A.M.’s between 5 and -17 and prove that their sum is ten tim...

    Text Solution

    |

  18. n arithmetic means are inserted between 3 and 17 such that ratio of fi...

    Text Solution

    |

  19. If a, b, c are in A.P., then prove that : (a-c)^2 =4(b^2 -ac).

    Text Solution

    |

  20. If a, b, c are in A.P., prove that : a^3+4b^3+c^3=3b (a^2+c^2).

    Text Solution

    |