Given:
The given sequence is:
[tex]5,-2,-9,...[/tex]
To find:
The recursive formula for [tex]a_n[/tex], the nth term of the sequence.
Solution:
We have,
[tex]5,-2,-9,...[/tex]
Here, the first term is 5.
[tex]-2-5=-7[/tex]
[tex]-9-(-2)=-9+2[/tex]
[tex]-9-(-2)=-7[/tex]
The common difference is -7.
The recursive formula for the nth term of the sequence is
[tex]a_n=a_{n-1}+d[/tex]
Where, [tex]d[/tex] is the common difference.
Putting [tex]d=-7[/tex] in the above formula, we get
[tex]a_n=a_{n-1}+(-7)[/tex]
[tex]a_n=a_{n-1}-7[/tex]
Therefore, the recursive formula for the nth term of the sequence is [tex]a_n=a_{n-1}-7[/tex].
