Question

The natural numbers are grouped as follows:
$S_1=\left\{1\right\},S_2=\left\{2,3,4\right\},S_3=\left\{5,6,7,8,9\right\},...$, then the first element of $S_{21}$ is

• A. $391$
• B. $399$
• C. $401$
• D. $442$

Answer 1

Answer: (C)

The given groups of numbers can be arranged as

Number of terms upto $S_{20}=1+3+5+....$ to $20$ terms
$=\frac{20}{2}\left[2+\left(19\right)2\right]=400$
$\therefore S_{12}$ starts with $401$.