Question

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

(QUESTION 4.02)

Answer 1

Answer: a1=3; an=an−1+4

Explanation:

Answer 2

`a_(n+1)=a_n+4`

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`"