Q. The sum of a GP with common ratio 3 is 364 and last term is 243, then the number of terms is
A) $6$
B) $5$
C) $4$
D) $10$
Explanation
(a)
Given, $S_{n} = \frac{lr - a}{r - 1} = 364$
$\Rightarrow \ \frac{3 \times 243 - a}{2} = 364\ \Rightarrow a = 1$
Since, $l = ar^{n - 1} \Rightarrow 243 = 1(3)^{n - 1}$
$\Rightarrow \ 3^{5} = 3^{n - 1} \Rightarrow n = 6$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.