Question

A recursive rule for an arithmetic sequence is a1=4;an=an−1+3 . What is an explicit rule for this sequence? Enter your answer in the box. an=

Answer 1

an=3n+1

Explanation:

Answer 2

`a_(n)=4+3(n-1)`

Explanation:

The given recursive rule is

`a_(1)=4\\a_(n)=a_(n-1)+3`

According to this recursive rule, the sequence is

`4, 7, 10, 13, 16, 19,...`

Because, the recursive rule states that each new term must be 3 units greater.

Now, an explicit form of this sequence could be found using this formula

`a_(n)=a_(1)+(n-1)d`

Where
`d=3` and
`a_(1)=4`

Replacing these values, we have

`a_(n)=4+3(n-1)`

Therefore, the explict form is
`a_(n)=4+3(n-1)`, which can be used to find any tem of the arithmetic sequence.