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Let S_n be the sum of the first n terms of an AP. If S_ 2 n =3 n+14 n^2 , then what is the common difference?

Options

  1. A5
  2. B6
  3. C7
  4. D9

Correct answer

C. 7

Step-by-step solution

aligned & S_ 2 n =3 n+14 n^2 & S_n=3 n 2 +14 ( n 2 )^2 & S_n= 3 n+7 n^2 2 & S₁= 3+7 2 =5=T₁ & S₂= 6+28 2 =17=T₁+T₂ & (T₁+T₂ )- (T₁ )=17-5=12 & T₂=12 & d=T₂-T₁=12-5=7 aligned

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