Home
Class 11
MATHS
If s1 ,s2 and s3 are the sum of first n,...

If `s_1 ,s_2` and `s_3` are the sum of first n,2n,3n terms respectively of an arithmetic progression, then show that `s_3=3(s_2-s_1)`.

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    PATHFINDER|Exercise QUESTION BANK|41 Videos

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

Similar Questions

Explore conceptually related problems

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)

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

If s_1 , s_2 , s_3 are thesums of n natural numbers, theirsquares, their cubes respectively. Show.that 9s_2^2=s_3(1+8s_1)

If S_(n) be the sum of first n terms of a G.P. whose common ratio is r, then show that, (r-1)(dS_(n))/(dr)=(n-1)S_(n)-nS_(n-1)

The sum of n ,2n ,3n terms of an A.P. are S_1S_2, S_3, respectively. Prove that S_3=3(S_2-S_1)dot

If s_1 be the sum of (2n+1) terms of an A.P and s_2 be the sum its odd terms, then prove that s_1:s_2=(2n+1):(n+1)

If S be the sum of first (2n+1) terms of an A.P and the sum of terms in odd positions of these (2n+1) terms be S', then show that (n+1)S = (2n+1)S'.

Let S_n denote the sum of first n terms of an A.P. If S_(2n)=3S_n , then find the ratio S_(3n)//S_ndot

If S_(1), S_(2), S_(3) are the sums of n natural numbers, their squares, their cubes respectively show that 9S_(2)^(2) = S_(3)(1+8S_(1)) .

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. N arithmetic means are inserted in between x and 2y and then between 2...

    Text Solution

    |

  2. Let Sn denote the sum upto n terms of an AP . If Sn=n^2P and Sm=m^2P ...

    Text Solution

    |

  3. If s1 ,s2 and s3 are the sum of first n,2n,3n terms respectively of an...

    Text Solution

    |

  4. Let a1,a2 ,a3 ...... be an A.P. Prove that sum(n=1)^(2m)(-1)^(n-1)an^2...

    Text Solution

    |

  5. A G.P. consists of 2n terms . If the sum of the terms occupying the od...

    Text Solution

    |

  6. If G1 ,G2 are geometric means , and A is the arithmetic mean between ...

    Text Solution

    |

  7. Show that abs((a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,0):}=0 ...

    Text Solution

    |

  8. If Sn=1+1/2+1/2^2+........+1/2^(n-1) . Calculate the least value of n ...

    Text Solution

    |

  9. Prove that the number of the sequence 121,12321,1234321,...... are eac...

    Text Solution

    |

  10. Find the sum of n terms of series 1+5((4n+1)/(4n-3))+9((4n+1)/(4n-3))^...

    Text Solution

    |

  11. Find the sum of the products of the integers 1,2,3,....n taken two at ...

    Text Solution

    |

  12. Sum the series n+(n-1)x+(n-2)x^2+.......+2x^(n-2)+x^(n-1).

    Text Solution

    |

  13. Find 1+2^2x+3^2x^2+4^2x^3+.... to infty absx lt 1.

    Text Solution

    |

  14. Find the sum of 1st n terms of the sequence 3,6,15,42,123,...

    Text Solution

    |

  15. Let Sn denote the sum of first n terms of the sequence 1,5,14,30,55,.....

    Text Solution

    |

  16. Finds the sum of first n terms of the series 3/(1^2xx2^2)+5/(2^2xx3^2)...

    Text Solution

    |

  17. How many terms of the series 54+51+48+45+ ... must be taken to make 51...

    Text Solution

    |

  18. If (b+c),(c+a),(a+b) are in H.P. show that a^2 ,b^2 , c^2 are in A.P.

    Text Solution

    |

  19. Find the sum of first n terms of the series 3/1^2+5/(1^2+2^2)+7/(1^2+2...

    Text Solution

    |

  20. If 0 < theta < pi/2 then find the least value of tantheta+cottheta

    Text Solution

    |