Question

The explicit rule for a sequence is given. an=4n−1 What is the recursive rule for the sequence?

Answer 1

Answer:

$a_{n+1}=a_n+4$

Step-by-step explanation:

Have in mind the definition of the term $a_n=4\,n-1$, and now work on what the term $a_{n+1}$ is based on the previous definition:

$a_{n+1} = 4\,(n+1)-1\\a_{n+1}=4\,n+4-1$

In the next step do NOT combine the numerical values, but try to identify the $a_n$ term ($4\,n-1$) in the expression (notice the use of square brackets to group the relevant terms):

$a_{n+1}=4\,n+4-1\\a_{n+1}=[4\,n-1]+4\\a_{n+1}=a_n+4$

So now we have the term "$a_{n+1}$" defined in a recursive manner based on the previous term "$a_n$"