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If S _ n = nP + n ( n -1) Q 2 , where S _ n denotes the sum of the first n terms of an AP , then the common difference is

Options

  1. AP + Q
  2. B2 P +3 Q
  3. C2 Q
  4. DQ

Correct answer

D. Q

Step-by-step solution

S _ n = np + n ( n -1) Q 2 We know, T ₁= S ₁ and T ₂= S ₂- S ₁ Common difference ( d )= T ₂- T ₁ S ₁=(1) P + 1(1-1) Q 2 = P +0= P S ₂=(2) P + 2(2-1) Q 2 =2 P + 2 Q 2 =2 P + Q . aligned & T ₁= P ; T ₂=2 P + Q - P = P + Q & Common difference ( d )= T ₂- T ₁ aligned = P + Q - P = Q

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