Q. The sets $S_{1},S_{2},S_{3}\ldots$ are given by $S_{1} = \left\{ \frac{2}{1} \right\},\ S_{2} = \left\{ \frac{3}{2},\frac{5}{2} \right\},\ S_{3} = \left\{ \frac{4}{3},\frac{7}{3},\frac{10}{3} \right\},\ S_{4} = \left\{ \frac{5}{4},\frac{9}{4},\frac{13}{4},\frac{17}{4} \right\},\ldots$ Then, the sum of the numbers in the set $S_{25}$ is
A) 320
B) 322
C) 324
D) 326
Explanation
(d)
As, $S_{25} = \left\{ \frac{26}{25},\frac{51}{25},\frac{76}{25},\ldots upto\ 25\ terms \right\}$
Here, $a = \frac{26}{25},\ \ n = 25,\ d = 1$
$\therefore S_{25} = \frac{25}{2}\left( \frac{52}{25} + 24 \right) = 326$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.