Question

If $t_n$ denotes $n^{th}$ term of the series $2+3+6+11+18+......$ then $t_{50}$ is

Answer 1

$\begin{array}{c}S=2+3+6+11+18+.........+T_n\\ S=\left(0^2+2\right)+\left(1^2+2\right)+\left(2^2+2\right)+........\left[{\left(T_{n-1}\right)}^2+2\right]\\ wefind\\ T_{50}={\left(T_{n-1}\right)}^2+2\\ ={\left(T_{50-1}\right)}^2+2\Rightarrow {\left(49\right)}^2+2\end{array}$