Question

Write a recursive function for each sequence.81,85,89,93,97

Answer 1

Okay, here we have this:

Considering the provided secuence: 81,85,89,93,97. Let's calculate the difference between each term to identify if it is constant or not:

85-81=4

89-85=4

93-89=4

97-93=4

Here we can see that the difference is a constant, so this mean that it's an Arithmetic sequence, now, let's replace in the formula:

$a_n=a_1+(n-1)d$

Replacing:

$a_n=81+(n-1)4$

And, turning this in a recursive function:

$g(n)=\begin{cases}81\text{ if n=}1 \\ g(n-1)+4\text{ if }n>1\end{cases}$