Given:
The given arithmetic sequence is:
[tex]-3,-1,1,3,...[/tex]
To find:
The recursive formula of the given arithmetic sequence.
Solution:
We have,
[tex]-3,-1,1,3,...[/tex]
Here, the first term is -3. So, [tex]b(1)=-3[/tex].
The common difference is:
[tex]d=-1-(-3)[/tex]
[tex]d=-1+3[/tex]
[tex]d=2[/tex]
The recursive formula of an arithmetic sequence is:
[tex]b(n)=b(n-1)+d[/tex]
Where, d is the common difference.
Putting [tex]d=2[/tex], we get
[tex]b(n)=b(n-1)+2[/tex]
Therefore, the recursive formula of the given arithmetic sequence is [tex]b(n)=b(n-1)+2[/tex], where [tex]b(1)=-3[/tex].
