The recursive definition used to generate the sequence {3, 6, 3, 6, 3,...} is:
where
and
<em><u>Solution:</u></em>
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
<em><u>So we can generate a recursive definition as:</u></em>
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