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The n th term of an AP. is 3+n 4 , then the sum of first 105 terms is

Options

  1. A270
  2. B735
  3. C1409
  4. D1470

Correct answer

D. 1470

Step-by-step solution

aligned & T _ n = 3+ n 4 & ~S _ n = _ n =0 ^ T _ n & = ( 3 4 + n 4 ) & = 3 4 n + 1 4 n ( n +1) 2 & = 7 8 n + n ^2 8 & ~S ₁₀₅= 7 8 105+ (105)^2 8 =1470 aligned

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