Home
Class 10
MATHS
The sum of n, 2n, 3n terms of an A.P. ar...

The sum of n, 2n, 3n terms of an A.P. are `S_1, S_2, S_3` respectively. Prove that `S_3 = 3(S_2 - S_1)`

Promotional Banner

Topper's Solved these Questions

  • AREAS RELATED TO CIRCLES

    RD SHARMA|Exercise All Questions|251 Videos

  • CIRCLES

    RD SHARMA|Exercise All Questions|131 Videos

Similar Questions

Explore conceptually related problems

If the sum of n,2n,3n terms of an AP are S_(1),S_(2),S_(3) respectively.Prove that S_(3)=3(S_(2)-S_(1))

Let the sum of n,2n,3n terms of an A.P.be S_(1),S_(2) and respectively,show that S_(3)=3(S_(2)-S_(1))

If the sum of n, 2n and infinite terms of G.P. are S_(1),S_(2) and S respectively, then prove that S_(1)(S_(1)-S)=S(S_(1)-S_(2)).

The sums of n terms of three arithmetical progressions are S_(1),S_(2) and S_(3). The first term of each unity and the common differences are 1,2 and 3 respectively.Prove that S_(1)+S_(3)=2S_(2)

If S_(1) be the sum of (2n+1) term of an A.P. and S_(2) be the sum of its odd terms then prove that S_(1):S_(2)=(2n+1):(n+1)

Let S_(n) denote the sum of the first n tem of an A.P.If S_(2n)=3S_(n) then prove that (S_(3n))/(S_(n))=6

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 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.

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,S_3,...,S_n be the sums of first n terms of n G.P.'s whose first terms are each unity and the common ratios are 1, 2, 3,.....,n respectively, prove that S_1+S_2+2S_3+3S_4+.........+(n-1)S_n=1^n+2^n+3^n+....+n^n.

RD SHARMA-ARITHMETIC PROGRESSIONS-All Questions
  1. How many terms of the series 54,51, 48,.. be taken so that their sum i...

    Text Solution

    |

  2. Find the number of terms in the series 20 ,19 1/3,18 2/3... the sum of...

    Text Solution

    |

  3. The sum of n, 2n, 3n terms of an A.P. are S1, S2, S3 respectively. Pro...

    Text Solution

    |

  4. The sums of n terms of three arithmetical progressions are S1, S2and ...

    Text Solution

    |

  5. If the sum of first m terms of an A.P. is the same as the sum of its f...

    Text Solution

    |

  6. The ratio of the sums of m and n terms of an A.P. is m^2: n^2 .Sho...

    Text Solution

    |

  7. A manufacturer of TV sets produced 600 sets in the third year and 700 ...

    Text Solution

    |

  8. A contract on construction job specifies a penalty for delay of com...

    Text Solution

    |

  9. A sum of Rs 280 is to be used to award four prizes. If each prize a...

    Text Solution

    |

  10. In a school students thought of planting trees in and around the sc...

    Text Solution

    |

  11. 200 logs are stacked in the following manner: 20 logs in the bottom ...

    Text Solution

    |

  12. The digits of a positive integer, having three digits, are in A.P. and...

    Text Solution

    |

  13. A man repays a loan of R s .3250 by paying R s .20 in the first month ...

    Text Solution

    |

  14. The houses of a row are numbered consecutively from 1 to 49. Show that...

    Text Solution

    |

  15. A ladder has rungs 25 cm apart, (see Figure). The rungs decrease un...

    Text Solution

    |

  16. A small terrace at a football ground comprises of 15 steps each of ...

    Text Solution

    |

  17. A spiral is made up of successive semicircles, with centres alterna...

    Text Solution

    |

  18. In a potato race, a bucket is placed at the starting point, which is ...

    Text Solution

    |

  19. Find the sum of the following arithmetic progressions: 50 ,\ 46 ,\ ...

    Text Solution

    |

  20. Find the sum of the following arithmetic progressions: 41 ,\ 36 ,\ ...

    Text Solution

    |