Given:
[tex]a_n=-5+2(n-1)[/tex]
To find:
The arithmetic sequence using a Recursive Formula.
Solution:
We have,
[tex]a_n=-5+2(n-1)[/tex] ...(i)
The explicit formula of an AP is
[tex]a_n=a_1+(n-1)d[/tex] ...(ii)
where, a₁ is first term and d is common difference.
From (i) and (ii), we get
[tex]a_1=-5,d=2[/tex]
Now, the recursive formula of an AP is
[tex]a_n=a_{n-1}+d[/tex]
Putting d=2, we get
[tex]a_n=a_{n-1}+2[/tex]
Therefore, the arithmetic sequence using a Recursive Formula is defined as [tex]a_n=a_{n-1}+2[/tex], where n>2 and [tex]a_1=-5[/tex].
