The recursive rule is
[tex]a_n=a_{n-1}+(-4)[/tex].
The iterative rule is
[tex]a_n=14-4n[/tex]
The recursive rule is given by the formula
[tex]a_n=a_{n-1}+d[/tex], where d is the common difference. Our common difference is -4, which gives us the recursive rule above.
The iterative rule begins with the formula
[tex]a_n=a_1+d(n-1)[/tex], where a₁ is the first term and d is the common difference. Our first term is 10 and our common difference is -4:
[tex]a_n=10+(-4)(n-1)
\\\text{Using the Distributive Property,}
\\
\\a_n=10+(-4*n)+(-4*-1)
\\
\\a_n=10-4n+4
\\
\\\text{Combining like terms,}
\\
\\a_n=14-4n[/tex]
