Verified Solution • 2025–26 Session moderate

QJEEM20Ma8a0d: JEE Main 2020 Mathematics - Class 11 JEEM20Ma8a0d Solution: The sum of the first three terms of a G.P. is S and their…

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

Multiple Choice Options

  • A [-3, ∞\infty )
  • B (- ∝\propto , 9]
  • C (- ∝\propto , -9] ∪\cup [-3, ∞\infty )
  • D (- ∝\propto , -3] ∪\cup [9, ∞\infty )

Step-by-Step Verified Solution

Let three terms of G.P. are ar{a \over r} , a, ar

∴\therefore a(1r+1+r)a\left( {{1 \over r} + 1 + r} \right) = S ...(1)

and a3 = 27

⇒\Rightarrow a = 3

∴\therefore 3(1r+1+r)3\left( {{1 \over r} + 1 + r} \right) = S

⇒\Rightarrow 1r+r=S3−1{{1 \over r} + r = {S \over 3} - 1}

⇒\Rightarrow As 1r+r≥2{{1 \over r} + r \ge 2} or 1r+r≤−2{{1 \over r} + r \le - 2}

∴\therefore S3−1≥2{{S \over 3} - 1 \ge 2} or S3−1≤−2{{S \over 3} - 1 \le - 2}

⇒\Rightarrow S3≥3{{S \over 3} \ge 3} or S3≤−1{{S \over 3} \le - 1}

⇒\Rightarrow S ≥\ge 9 or S ≤\le -3

∴\therefore S ∈\in (- ∝\propto , -3] ∪\cup [9, ∞\infty )

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