Question

Please help me... and explain it, I don't know how to do it

Answer 1

`n^(th)\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^(th)\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=-3\\ d=4\\ a_n=193 \end{cases} \\\\\\ 193=-3+(n-1)4\implies 193=-3+4n-4\implies 193=-7+4n \\\\\\ 200=4n\implies \cfrac{200}{4}=n\implies 50=n`