Home
Class 10
MATHS
If Sn denotes the sum of first n term...

If `S_n` denotes the sum of first `n` terms of an A.P., prove that `S_(12)=3(S_8-S_4)` .

Text Solution

AI Generated Solution

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 S_(n) denotes the sum of first n terms of an AP, then prove that S_(12)=3(S_(8)-S_(4)).

If S_(n) denotes the sum of the first n terms of an A.P.prove that S_(30)=3(S_(20)-S_(10)).

If S_(n) denotes the sum of first n terms of an A.P., then (S_(3n)-S_(n-1))/(S_(2n)-S_(n-1)) is equal to

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))

If S_(n) denotes the sum of first n terms of an A.P. If S_(2n) = 5(S_n) , then prove (S_(6n))/(S_(3n))=17/8

If S_(n), denotes the sum of n terms of an A.P. then S_(n+3)-3S_(n+2)+3S_(n+1)-S_(n)=

If S_(n) denote the sum of first n terms of an A.P. whose first term is a and S_(nx)/S_(x) is independent of x, then S_(p)=p^(3) b.p^(2)a .pa^(2) d.a^(3)

If S_n denotes sum of first n terms of an A.P. such that, S_(20) = 790, S_(10) = 145 then S_(15) - S_5

S_(r) denotes the sum of the first r terms of an AP.Then S_(3d):(S_(2n)-S_(n)) is -

If S_r denotes the sum of the first r terms of an A.P. Then, S_(3n)\ :(S_(2n)-S_n) is n (b) 3n (c) 3 (d) none of these

RD SHARMA-ARITHMETIC PROGRESSIONS-All Questions
  1. If the 10 t h term of an A.P. is 21 and the sum of its first ten te...

    Text Solution

    |

  2. The first and the last terms of an AP are 7 and 49 respectively. If...

    Text Solution

    |

  3. If Sn denotes the sum of first n terms of an A.P., prove that S(...

    Text Solution

    |

  4. If the sum of the first n terms of an A.P. is 1/2(3n^2+7n), then find ...

    Text Solution

    |

  5. The sum of first 9 terms of an A.P. is 162. The ratio of its 6th t...

    Text Solution

    |

  6. Define an arithmetic progression.

    Text Solution

    |

  7. Write the common difference of an A.P. whose n t h term is an=3n+7 ...

    Text Solution

    |

  8. Which term of the sequence 114 ,\ 109 ,\ 104 ,\ is the first ne...

    Text Solution

    |

  9. Write the value of a(30)-a(10) for the A.P. 4,\ 9,\ 14 ,\ 19 ,\ ...

    Text Solution

    |

  10. Write 5t h term from the end of the A.P. 3,\ 5,\ 7,\ 9,\ ddot,\ 201...

    Text Solution

    |

  11. Write the value of x for which 2x ,\ x+10 and 3x+2 are in A.P.

    Text Solution

    |

  12. Write the n t h term of an A.P. the sum of whose n terms is Sn .

    Text Solution

    |

  13. Write the sum of first n odd natural numbers.

    Text Solution

    |

  14. Write the sum of first n even natural numbers.

    Text Solution

    |

  15. If the sum of n terms of an A.P. is Sn=3n^2+5n . Write its co...

    Text Solution

    |

  16. Write the expression for the common difference of an A.P. whose fir...

    Text Solution

    |

  17. First the term of an A.P is p and its common difference is q. Find its...

    Text Solution

    |

  18. For what value of p are 2p+1,\ 13 ,\ 5p-3 are three consecutive ...

    Text Solution

    |

  19. If 4/5,\ a ,\ 2 are three consecutive terms of an A.P., then find t...

    Text Solution

    |

  20. If the sum of first p terms of an AP is ap^2+bp find the common differ...

    Text Solution

    |