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Let Vr denote the sum of the first r ter...

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`

Answer

Step by step text solution for 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 by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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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, …. T_(r) is always

    A
    an odd number
    B
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    C
    a prime number
    D
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    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 f(x) = px^(2) + qx + r , where p, q and r are in A.P. If f(1) = 3 , then which of the following is correct?

    A
    `q=1`
    B
    `p + q =1`
    C
    `p - r = 1`
    D
    none of these

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