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JEE Main20238 Apr 2023Evening ShiftMathematicsSequences and SeriesActual

Let a n be n th term of the series 5 + 8 + 14 + 23 + 35 + 50 + . . . . . . . and S n = ∑ k = 1 n a k . Then S 30 - a 40 is equal to

Options

  1. A11310
  2. B11260
  3. C11290
  4. D11280

Correct answer

C. 11290

Step-by-step solution

The given series is a n , then we can write as a n = 5 + 8 + 14 + 23 + . . . . . . . . . . . . + a n a n =             5 + 8 + 14 + 23 + . . . . . . + a n - 1 + a n Subtracting above equations, we get 0 = 5 + 3 + 6 + 9 + . . . . + a n - a n - 1 - a n ⇒ a n = 5 + n - 1 2 2 × 3 + n - 1 - 1 3 ⇒ a n = 5 + n - 1 2 3 n ⇒ a n = 1 2 3 n 2 - 3 n + 10 So, ⇒ a 40 = 1 2 3 × 40 2 - 3 × 40 + 10 ⇒ a 40 = 1 2 4800 - 120 + 10 ⇒ a 40 = 2345 ⇒ S 30

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