Question

What is the recursive rule for
`a_(n)`=2n+11?

Answer 1

Your answer is .a1=13;an=an−1+2

Explanation:

Answer 2

`a_(1)=13;a_(n)=a_(n-1)+2`

Explanation:

The given equation is

`a_(n)=2n+11`

It's important to know that a recursive formula shows two important characteristics.

1. The first term of the sucesion.
2. The rule or pattern to obtain any term greater than the first term.

So, in this case, we first need to find the first term of the given sequence, that is, when
`n=1`

`a_(n)=2n+11\\a_(1)=2(1)+11=2+11=13`

So, the possible answers are the first and third choices.

Now, the following term would be when
`n=2`

`a_(n)=2n+11\\a_(2)=2(2)+11=4+11=15`

As you can see, the second term is 2 units greater than the first term. That means the right answer is the third choice, because it has a positive term of two units.

`a_(1)=13;a_(n)=a_(n-1)+2`

Let's try for
`n=2`

`a_(2)=13+2=15`

Therefore, the answer is

`a_(1)=13;a_(n)=a_(n-1)+2`