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

  • ANNUAL EXAMINATION QUESTION PAPERS 2015

    UNITED BOOK HOUSE|Exercise EXERCISE|49 Videos

  • ANNUAL EXAMINATION QUESTION PAPERS 2017

    UNITED BOOK HOUSE|Exercise EXERCISE|50 Videos

Similar Questions

Explore conceptually related problems

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)) .

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 the first term, common ratio and the sum of first n terms of a G.P. be a, r and S_(n) respectively, find the value of S_(1) + S_(2) + S_(3) +….+S_(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) .

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) .

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 sum of first n natural numbers, their squares and their cubes, respectively , show that 9 S_(2)^(2) = S_(3) (1+ 8S_1)

Let S_(n) be the sum of first n terms of an A.P. If S_(2n) = 5s_(n) , then find the value of S_(3n) : S_(2n) .

If S_1, S_2 and S_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_1,S_2 and S_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

UNITED BOOK HOUSE-ANNUAL EXAMINATION QUESTION PAPERS 2016-EXERCISE
  1. Find the (r+1)th term from the end in the expansion of (1-3x)^n.

    Text Solution

    |

  2. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

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

    Text Solution

    |

  4. Find the locus of the mid-point of the portion of the line x cosalpha+...

    Text Solution

    |

  5. If the coordinates of a point lies on the ellipse 9x^2+16y^2=144 be (2...

    Text Solution

    |

  6. If y=e^x/(1+x^2),determin dy/dx.

    Text Solution

    |

  7. Evaluate :lim(xrarrpi/4)(1-tanx)/(x-pi/4)

    Text Solution

    |

  8. can 7/2be the probability of an event? Explain.

    Text Solution

    |

  9. Two variables x and y are related by y=10-3x.If the standard deviation...

    Text Solution

    |

  10. For any three sets A,B and C prove that Acup(BcapC)=(AcupB)cap(AcupC)

    Text Solution

    |

  11. Find the value of 16cos(pi/15).cos((2pi)/15).cos((4pi)/15).cos((8pi)/1...

    Text Solution

    |

  12. Show that sin^3alpha+sin^3(120^@+alpha)+sin^3(240^@+alpha)=-3/4sin3alp...

    Text Solution

    |

  13. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

  14. If the P^(th)and q^(th)terms of an A.Pare a and b respectively,then sh...

    Text Solution

    |

  15. Find the probability of drawing 4 cards from a pack of 52 cards such t...

    Text Solution

    |

  16. Find the sum of n-terms of the following series:(x+1/x)^2+(x^2+1/x^2)^...

    Text Solution

    |

  17. The equations of two sides of a square are 5x+12y-10=0 and 5x+12y+29=0...

    Text Solution

    |

  18. Find the equation of the circle passes through the points (4,3) and (-...

    Text Solution

    |

  19. Show that the area of the triangle formed by the lines y = m(1) x + c(...

    Text Solution

    |

  20. Find the value of cos B for the triangle formed by joining the points ...

    Text Solution

    |