Home
Class 12
MATHS
Let Vr denote the sum of first r terms o...

Let Vr denote the sum of first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is (2r – 1).
Let `T_(r)=V_(r+1)-V_(r)-2 and Q_(r+1)-T_(r)` for `r=1,2…….`

1. The sum `V_(1)+V_(2)+….+V_(n)` is
A. `(1)/(12) n(n+1)(3n^2-n+1)`
B. `(1)/(12)n(n+1)(3n^2+n+2)`
C. `(1)/(2)n(2n^2-n+1)`
D. `(1)/(2)(2n^3-2n+3)`.

2. Let `T_r=V_(r+1)-V_r-2` and `Q_r =T_(r+1)-T_r` for `r=1,2` `T_r` is always
(A) an odd number
(B) an even number
(C) a prime number
(D) a composite number

Promotional Banner

Topper's Solved these Questions

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -4 Level -I Previous Year /JEE Main|19 Videos
  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE 4 (PREVIOUS YEAR| JEE MAIN)|25 Videos
  • SOLUTION OF TRIANGLE

    MOTION|Exercise EXERCISE - 4( LEVEL II)|10 Videos

Similar Questions

Explore conceptually related problems

Let V_r denote the sum of the first' ' terms of an arithmetic progression (A.P.) whose first term is'r and the common difference is (2r-1). Let T_r=V_(r+1)-V_r -2 and Q_r=T_(r+1) -T_r for r=1,2,....... The sum V_1+V_2+......+V_n is

Let V_r denote the sum of the first r terms of an arithmetic progression (AP) whose first term is r and the common difference is (2r-1) . Let T_r=V_(r+1)-V_r-2 and Q_r =T_(r+1)-T_r for r=1,2 T_r is always (A) an odd number (B) an even number (C) a prime number (D) a composite num,ber

Let T_(r) be the rth term of an A.P.whose first term is -1/2 and common difference is 1, then sum_(n)^(n)sqrt(1+T_(r)T_(r+1)T_(r+2)T_(r+3))

Let T_(r) be the r^(th) term of an A.P whose first term is a and common difference is d IF for some integer m,n,T_(m)=(1)/(n) and T_(n)=(1)/(m) then a-d=

Let V_r denote the sum of the first r terms of an arithmetic progression (AP) whose first term is r and the common difference is (2r-1) . Let T_r=V_(r+1)-V_r-2 and Q_r =T_(r+1)-T_r for r=1,2 Which one of the following is a correct statement? (A) Q_1, Q_2, Q_3………….., are in A.P. with common difference 5 (B) Q_1, Q_2, Q_3………….., are in A.P. with common difference 6 (C) Q_1, Q_2, Q_3………….., are in A.P. with common difference 11 (D) Q_1=Q_2=Q_3

If S_(n) denotes the sum fo n terms of a G.P. whose first term and common ratio are a and r respectively then show that: S_(1)+S_(3)+S_(5)+……..+S_(2n)-1=(an)/(1-r)-(ar(1-r^(2n)))/((1-r^(2))

If sum of x terms of a series is S_(x)=(1)/((2x+3)(2x+1)) whose r^(th) term is T_(r) . Then, sum_(r=1)^(n) (1)/(T_(r)) is equal to

MOTION-SEQUENCE & SERIES -Exercise -4 Level -II Previous Year /JEE Advanced
  1. Let Vr denote the sum of first r terms of an arithmetic progression (A...

    Text Solution

    |

  2. Let Vr denote the sum of the first r terms of an arithmetic progressio...

    Text Solution

    |

  3. Let Vr denote the sum of the first r terms of an arithmetic progressio...

    Text Solution

    |

  4. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

    Text Solution

    |

  5. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

    Text Solution

    |

  6. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

    Text Solution

    |

  7. A straight line through the vertex P of a triangle PQR intersects the ...

    Text Solution

    |

  8. Suppose four distinct positive numbers a1,a2,a3,a4 are in G.P. Let b1=...

    Text Solution

    |

  9. In the sum of first n terms of an A.P. is cn^2, then the sum of square...

    Text Solution

    |

  10. Let Sk ,k=1,2, ,100 , denotes thesum of the infinite geometric series ...

    Text Solution

    |

  11. Let a(1),a(2),a(3),"........."a(11) be real numbers satisfying a(1)=15...

    Text Solution

    |

  12. The minimum value of the sum of real number a^(-5),a^(-4),3a^(-3),1,a^...

    Text Solution

    |

  13. Let a1, a2, a3, ,a(100) be an arithmetic progression with a1=3a n dsp...

    Text Solution

    |

  14. If a(1),a(2),a(3),"......" be in harmonic progression with a(1)=5 and ...

    Text Solution

    |

  15. Let a(n) denote the number of all n-digit numbers formed by the digits...

    Text Solution

    |

  16. Let an denote the number of all n-digit positive integers formed by th...

    Text Solution

    |

  17. Let S(n)=sum(k=1)^(4n)(-1)^((k(k+1))/2)k^(2). Then S(n) can take value...

    Text Solution

    |

  18. A pack contains n cards numbered from 1 to n. Two consecutive numbered...

    Text Solution

    |

  19. Let a,b,c be positive integers such that (b)/(a) is an integer. If a,b...

    Text Solution

    |

  20. Suppose that all the terms of an arithmetic progression (A.P.) are nat...

    Text Solution

    |