The sum of the first three terms of G . P is S   and their products is 27 . Then all such S lie in

The sum of the first three terms of G.P is S and their products is 27. Then all such S lie in

  1. (-∞,-9]∪[3,∞)
  2. [-3,∞)
  3. (-∞,-3]∪[9,∞)
  4. (-∞, 9]

Solution

 Let terms are ar,a,ar

then a3=27  ⇒a=3

Now S=3r+3+3r

S=31r+r+3

r+1r≥2 ∀r>0 or r+1r≤-2 ∀r<0

S∈(-∞,-3]∪[9,∞)

Asked in: JEE Main 2020 (02 Sep Shift 1)

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