Typing sequences recursively in Overleaf

Question

I'm trying to type the following sequence recursively on Overleaf but I'm not exactly sure how to format it exactly as it is shown below. More specifically, I need help on how to type the info past the left brace.

Answer 1

You can define a new type of cases using mathtools:

\documentclass{article}
\usepackage{mathtools}
\makeatletter
\newcases{centercases}{\quad}
  {\hfil$\m@th\displaystyle{##}$\hfil}
  {$\m@th\displaystyle{##}$\hfil}{\lbrace}{.}
\makeatother
\begin{document}
[
a_{n}=
\begin{centercases}
  1         & n=1 \
  a_{n-1}+4 & n>1
\end{centercases}
]
\end{document}

However, the output obtained with cases is more frequently used: