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Given that a 4 + a 8 + a 12 + a 16 = 224 , the sum of the first nineteen terms of the arithmetic progression a 1 , a 2 , a 3 , . . . . . is equal to

Options

  1. A1540
  2. B1064
  3. C3125
  4. D1980

Correct answer

B. 1064

Step-by-step solution

a 1 , a 2 , a 3 , . . . . . . , a 19 are in A . P . ⇒ S = a 1 + a 2 + . . . . . . + a 18 + a 19 = 19 2 a 1 + a 19 Given, a 4 + a 8 + a 12 + a 16 = 224 ⇒ a 1 + 3 d + a 1 + 7 d + a 19 - 7 d + a 19 - 3 d = 224 ⇒ 2 a 1 + a 19 = 224 ⇒ a 1 + a 19 = 112 ⇒ 19 2 a 1 + a 19 = 19 2 × 112 ⇒ S = 19 2 × 112 = 19 × 56 = 1064

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