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If n^ th term of the series 6+17+34+57+ . is ( ₂ a ) n^2+ ( ₃(b-a) )_n+ ₄ c , then:

Options

  1. Aa+b=5
  2. B₅(2 c+b)= ₅(a+b)
  3. Cb-c=13
  4. D₂(2 c+a)=4

Correct answer

D. ₂(2 c+a)=4

Step-by-step solution

S_n=6+17+34+57+ +T_n Sub S_n=6+17+34+57+ +T_ n-1 +T_n 0=6+11+17+23+ + (T_n-T_ n-1 )-T_n aligned & T_n=6+11+17+23+ + (T_n-T_ n-1 )=6+ n-1 2 (2 11+(n-1-1) 6) & T_n=6+(n-1)(3 n+5) & T_n=3 x^2+2 x+1 ( ₂ a ) n^2+ ( ₃(b-a) ) n+ ₄ c aligned array ll & ₂ a=3 a=8 ; ₃(b-a)=2 b-a=9 b=17 & ₄ c=1 c=4 array Now, verify the options.

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