Verified Solution • 2025–26 Session moderate

QJEEM20Ma888b: JEE Main 2020 Mathematics - Class 11 JEEM20Ma888b Solution: If the sum of the second, third and fourth terms of a positive…

If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eighth terms is 243, then the sum of the first 50 terms of this G.P. is :

Multiple Choice Options

  • A 213(350−1){2 \over {13}}\left( {{3^{50}} - 1} \right)
  • B 113(350−1){1 \over {13}}\left( {{3^{50}} - 1} \right)
  • C 126(349−1){1 \over {26}}\left( {{3^{49}} - 1} \right)
  • D 126(350−1){1 \over {26}}\left( {{3^{50}} - 1} \right)

Step-by-Step Verified Solution

Let first term = a > 0

Common ratio = r > 0

ar + ar2 + ar3 = 3 ....(i)

ar5 + ar6 + ar7 = 243 ....(ii)

⇒\Rightarrow r4(ar + ar2 + ar3) = 243

⇒\Rightarrow r4(3) = 243

⇒\Rightarrow r = 3 as r > 0

from (i)

3a + 9a + 27a = 3

⇒\Rightarrow a = 113{1 \over {13}}

∴\therefore S50 = a(r50−1)(r−1){{a\left( {{r^{50}} - 1} \right)} \over {\left( {r - 1} \right)}}

= 126(350−1){1 \over {26}}\left( {{3^{50}} - 1} \right)

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