A sequence is defined recursively by the formula f(n + 1) = f(n) + 3 . The first term of the sequence is –4. What is the next term in the sequence?
using n notation is just a fancy way of describing a sequence.
n is the number you're currently at, so with that logic n+1 is the term after it in the sequence.
f(n) is the function using n as the input.
so you know that the first term of the sequence is -4, or f(n)= -4.
In order to find f(n+1) plug in what you know for f(n). $${f}{\left({\mathtt{n}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)} = {f}{\left({\mathtt{n}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}$$ we know that f(n) = -4, so it is substituted in to the equation given. $${f}{\left({\mathtt{n}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)} = {\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}$$ now simplify! $${f}{\left({\mathtt{n}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)} = -{\mathtt{1}}$$ hope this helps!