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 se

Or just:

 

f(1) = -4

 

f(2) = f(1) + 3   so f(2) = -4 + 3  or f(2) = -1

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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!