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The common difference of the A.P.: a₁, a₂, , a_ m is 13 more than the common difference of the A.P.: b₁, b₂, , b_ n . If b₃₁=-277, b₄₃=-385 and a₇₈=327 , then a₁ is equal to

Options

  1. A16
  2. B21
  3. C19
  4. D24

Correct answer

C. 19

Step-by-step solution

Let d and d' be the common differences of the two APs respectively. Given: d = d' + 13 . From the second AP: b₄₃ - b₃₁ = 12d' , so -385 - (-277) = 12d' , giving -108 = 12d' and d' = -9 . Therefore d = -9 + 13 = 4 . For the first AP: a₇₈ = a₁ + 77d , so 327 = a₁ + 77(4) = a₁ + 308 . Thus a₁ = 19

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