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Let p, q and 3 be respectively the first, third and fifth terms of an A.P. Let d be the common difference. If the product (p q) is minimum, then what is the value of d ?

Options

  1. A1
  2. B3 8
  3. C9 8
  4. D9 4

Correct answer

C. 9 8

Step-by-step solution

Given that a=P, a₃=P+2 d=q ....(i) aligned & a₅=P+4 d=3 P=3-4 d & q=3-4 d+2 d=3-d[ from (i) ] & Now let S=P q=(3-4 d)(3-2 d) & S=8 d^2-18 d+9 & d s d d =16 d-18=0 & d= 9 8 & d^2 s d d^2 =16 0 & P q is minimum when d= 9 8 . aligned

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