If T$_n$ denotes the $\mathrm{n}^{ ext {th }}$ term of the sequence $2,3,6,11,18, \ldots$ then $\ma

Question

If T$_n$ denotes the $\mathrm{n}^{	ext {th }}$ term of the sequence $2,3,6,11,18, \ldots$ then $\mathrm{T}_{50}$ is equal to

Professor PC Thomas Classes · Answer

$ \begin{aligned} & \mathrm{S}_{\mathrm{n}}=2+3+6+11+18+\ldots+\mathrm{t}_{\mathrm{n}-1}+\mathrm{t}_{\mathrm{n}} \ & \frac{\mathrm{~S}_{\mathrm{n}}=2+3+6+11+\mathrm{t}_{\mathrm{n}-2}+\mathrm{t}_{\mathrm{n}-1}+\mathrm{t}_{\mathrm{n}}}{0=2+[1+3+5+\ldots(\mathrm{n}-1) 	ext { terms }]-\mathrm{t}_{\mathrm{n}}} \ & \mathrm{t}_{\mathrm{n}}-2=\frac{\mathrm{n}-1}{2}[2(1)+(\mathrm{n}-2) 2]=\frac{(\mathrm{n}-1)^2}{1} \ & \mathrm{t}_{50}=49^2+2 \end{aligned} $