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JEE Main20236 Apr 2023Morning ShiftMathematicsSequences and SeriesActual

The sum of the first 20 terms of the series 5 + 11 + 19 + 29 + 41 + . . . is

Options

  1. A3520
  2. B3450
  3. C3250
  4. D3420

Correct answer

A. 3520

Step-by-step solution

Let the given series be S n , then we can write as S n = 5 + 11 + 19 + 29 + 41 + . . . . . . . . . . . . + T n S n =                 5 + 11 + 19 + 29 + 41 + . . . . . . + T n - 1 + T n Subtracting above equations, we get 0 = 5 + 6 + 8 + 10 + . . . . - T n ⇒ T n = 5 + n - 1 2 12 + n - 2 2 ⇒ T n = 5 + n - 1 n + 4 ⇒ T n = n 2 + 3 n + 1 So, S 20 = ∑ n = 1 20 T n ⇒ S 20 = ∑ n = 1 20 n 2 + 3 n + 1 ⇒ S 20 = 20 × 21 × 41 6 + 3 &#215

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