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If a₁, a₂, a₃, , a_n, . are in A.P. such that a₄-a₇+a₁₀=m , then the sum of first 13 terms of this A.P., is :

Options

  1. A10 ~m
  2. B12 ~m
  3. C13 ~m
  4. D15 ~m

Correct answer

C. 13 ~m

Step-by-step solution

If d be the common difference, then aligned m & =a₄-a₇+a₁₀=a₄-a₇+a₇+3 ~d =a₇ ~S ₁₃ & = 13 2 [a₁+a₁₃ ]= 13 2 [a₁+a₇+6 d ] & = 13 2 [2 a₇ ]=13 a₇=13 ~m aligned

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