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},....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 $