Which recursive definition could be used to generate the sequence {3, 6, 3, 6, }?

The recursive definition used to generate the sequence {3, 6, 3, 6, 3,...} is:

where and

Solution:

Given sequence is 3, 6, 3, 6, 3,...

To find: recursive definition for the sequence

First term in the sequence is 3

Then you add on 3 to get to 6 as the second term

Then add -3 to get 3 as third term

This pattern goes on forever

3 + 3 = 6

6 - 3 = 3

3 + 3 = 6

6 - 3 = 3

and so on

So we can generate a recursive definition as:

Let be the nth term and "n" denotes the term's location

is the first term of sequence

, where and

Here, is used to denote , we add on either +3 or -3 to the previous term to get next term