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