Question

The sets $S_1,S_2,S_3,....$ are given by
$S_1=\left\{\frac{2}{1}\right\},$
$S_2=\left\{\frac{3}{2},\frac{5}{2}\right\},S_3=\left\{\frac{4}{3},\frac{7}{3},\frac{10}{3}\right\},$
$S_4=\left\{\frac{5}{4},\frac{9}{4},\frac{13}{4},\frac{17}{4}\right\},....$
Then the sum of the numbers in the set $S_{25}$ is

• A. 320
• B. 322
• C. 324
• D. 325
• E. 326

Answer 1

Answer: (E)

According to given pattern
$S_{25}=\left\{\frac{26}{25},\frac{51}{25},\frac{76}{25},....upto25terms\right\}$
Here, $a=\frac{26}{25},n=25,d=1$
$\therefore$ $S_{25}=\frac{25}{2}\left[\frac{52}{25}+24\right]=326$