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

Answer

Step by step text solution for 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……. <BR>1. The sum V_(1)+V_(2)+….+V_(n) is <BR>A. (1)/(12) n(n+1)(3n^2-n+1) <BR>B. (1)/(12)n(n+1)(3n^2+n+2) <BR>C. (1)/(2)n(2n^2-n+1) <BR>D. (1)/(2)(2n^3-2n+3). <BR><BR>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 <BR>(A) an odd number <BR>(B) an even number <BR>(C) a prime number <BR>(D) a composite number by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

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

Knowledge Check

  • Let V_(r) denote the sum of the 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) = T_(r + 1) - T_(r) for r = 1, 2, …. 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)/(3) (2n^(3) - 2n + 3)`

  • Let V_(r) denote the sum of the 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) = 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

  • Let V_(r) denote the sum of the 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) = 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) = ……..`

    • Similar Questions

    Explore conceptually related problems

    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

    Home
    Profile