Question

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

Answer 1

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

`a_n = a_(n - 1) + 3(-1)^n` where
`a_1 = 3` and
`n\geq 2`

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
`a_n` be the nth term and "n" denotes the term's location

`a_1` is the first term of sequence

`a_n = a_(n - 1) + 3(-1)^n` , where
`a_1 = 3` and
`n\geq 2`

Here,
`3(-1)^n` is used to denote , we add on either +3 or -3 to the previous term to get next term