What is the recursive rule for an=2n+11?
a1=13;an=an−1+2
a1=13;an=an−1+11
a1=2;an=an−1+11
a1=11;an=an−1+2
@ms.sue
The recursive rule for an=2n+11 is a1=11;an=an−1+2.
The correct recursive rule for the given sequence an=2n+11 is:
a1=13; an=an−1+2
To explain how to find this recursive rule, let's break it down:
- The given sequence is an=2n+11.
- The subscript "n" represents the position of a term in the sequence.
- The term a1 represents the first term in the sequence, which is 13.
- The recursive rule should express how each subsequent term (an) is related to the previous term (an−1).
To find the recursive rule, we need to determine how each term is related to the previous term. In this case, we can see that each term is obtained by adding 2 to the previous term. Therefore, the recursive rule for this sequence is an=an−1+2.
In other words, to find each term in the sequence, you take the previous term and add 2. The first term (a1) is given as 13, and each subsequent term (an) can be found by adding 2 to the previous term (an−1).
a1 = 13
a2 = 15 = a1 + 2
a3 = 17 = a2 + 2
...
an = an-1 + 2 , n > 1