JEE Mains · Maths · STD 11 - 8. sequence and series
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
- A \(\frac{2}{13}\left(3^{50}-1\right)\)
- B \(\frac{1}{26}\left(3^{50}-1\right)\)
- C \(\frac{1}{13}\left(3^{50}-1\right)\)
- D \(\frac{1}{26}\left(3^{49}-1\right)\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{26}\left(3^{50}-1\right)\)
Step-by-step Solution
Detailed explanation
Let first term \(=a>0\) Common ratio \(=r>0\) \(ar + ar ^{2}+ ar ^{3}=3\) \(ar ^{5}+ ar ^{6}+ ar ^{7}=243\) \(r^{4}\left(a r+a r^{2}+a r^{3}\right)=243\) \(r^{4}(3)=243 \Rightarrow r=3\) as \(r>0\) from (1) \(3 a+9 a+27 a=3\) \(a=\frac{1}{13}\)…
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