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JEE Main20199 Jan 2019Morning ShiftMathematicsSequences and SeriesActual

Let a 1 , a 2 , … , a 30 be an A.P., S = ∑ i = 1 30 a i and T = ∑ i = 1 15 a ( 2 i - 1 ) . If a 5 = 27 and S - 2 T = 75 , then a 10 is equal to:

Options

  1. A52
  2. B47
  3. C42
  4. D57

Correct answer

A. 52

Step-by-step solution

Let common difference = d ∴ S =   ∑ i = 1 30 a i = 30 2 2 a 1 + 29   d ∴ S = 15   2 a 1 + 29   d . . . . . . . .   ( i ) T = 15 2 2 a 1 + 14   .   2 d T = 15   a 1 + 14 d   . . . . . . . . . . . ( i i ) a 1 + 4 d = 27 . . . . . . . . .   ( i i i ) S - 2 T = 75 ⇒ 15 2 a 1 + 29   d - 30   a 1 + 14 d   = 75 ⇒ 15   d 29 - 28 =   75 ⇒ d = 5 ∴   from ( i i i ) a 1 = 7 ∴   a 10 = a 1 + 9 d =

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