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In an A.P., the sixth term a 6 = 2 . If the a 1 a 4 a 5 is the greatest, then the common difference of the A.P., is equal to

Options

  1. A3 2
  2. B8 5
  3. C2 3
  4. D5 8

Correct answer

B. 8 5

Step-by-step solution

Given: a 6 = 2 . Also, a 1 a 4 a 5 is greatest. ⇒ a + 5 d = 2 . . . i Let, y = a 1 a 4 a 5 ⇒ y = a ( a + 3 d ) ( a + 4 d ) ⇒ y = ( 2 - 5 d ) ( 2 - 2 d ) ( 2 - d ) ⇒ y = 4 - 4 d - 10 d + 10 d 2 2 - d ⇒ y = 4 - 14 d + 10 d 2 2 - d ⇒ y = 8 - 4 d - 28 d + 14 d 2 + 20 d 2 - 10 d 3 ⇒ y = 8 - 32 d + 34 d 2 - 10 d 3 ⇒ y ' = - 32 + 68 d - 30 d 2 ⇒ y ' = - 2 15 d 2 - 34 d + 16 ⇒ y ' = - 2 ( 5 d - 8 ) ( 3 d - 2 ) So, the function attains maxima at d = 8 5

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