Verified Solution • 2025–26 Session moderate

QJEEM19Ma0622: JEE Main 2019 Mathematics - Class 11 JEEM19Ma0622 Solution: Let a 1 , a 2 , a 3 ,......be an A.P. with a 6 = 2. Then the…

Let a1, a2, a3,......be an A.P. with a6 = 2. Then the common difference of this A.P., which maximises the product a1a4a5, is :

Multiple Choice Options

  • A 32{3 \over 2}
  • B 65{6 \over 5}
  • C 85{8 \over 5}
  • D 23{2 \over 3}

Step-by-Step Verified Solution

first term = a, Common difference = d

∴\therefore a + 5d = 2

a1. a4. a5 = a(a + 3d) (a + 4d)

f(d) = (2 – 5d) (2 – 2d) (2 – d)

⇒\Rightarrow f′(d)=0⇒d=23,85f'(d) = 0 \Rightarrow d = {2 \over 3},{8 \over 5}

⇒\Rightarrow f''(d) < 0\,at\,d = {8 \over 5}

 ⇒d=85\, \Rightarrow d = {8 \over 5}

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