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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,berA. `Q_(1), Q_(2), Q_(3)`,.... are in an AP with common difference 5B. `Q_(1), Q_(2), Q_(3)`... are in an AP with common difference 6C. `Q_(1), Q_(2), Q_(3)`,.... are in an AP with common difference 11D. `Q_(1) = Q_(2) = Q_(3) = ...` |
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Answer» Correct Answer - B Since, `T_(r) = 3r^(2) + 2r -1` and `T_(r+1) = 3 (r +1)^(2) + 2(r +1) -1` `:. Q_(r) = T_(r +1) - T_(r) = 3 [2r + 1] + 2 [1]` `rArr Q_(r) = 6r + 5` `rArr Q_(r +1) = 6(r +1) + 5` Common difference `= Q_(r +1) - Q_(r) = 6` |
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