$\text{ If }{T}_n\text{ denotes the }{n}^{\text{fi }}\text{ term of the series }2+3+6+11+18+\dots \dots \text{ , then }{T}_{50}\text{ is }$

$\text{ Let }S=2+3+6+11+18+\dots .+T_n$

$\text{ Or }S= 2+3+6+11+\dots \dots +T_n$

$\text{ On subtracting. we get }$

$0=2+1+3+5+7+\dots -T_n$

$\Rightarrow T_n=2+[1+3+5+(n-1\left)term\right]$

          $=2+\frac{n-1}{2}[2+(n-1-1\left)2\right]$

$\Rightarrow T_n=2+(n-1{)}^2$

$\therefore T_{50}=2+(50-1{)}^2={49}^2+2$