ANSWER
The rule is:
[tex]a_{n}=49 - 20n[/tex]
The indicated term is:
[tex]a_{32}=-591[/tex]
EXPLANATION
The terms of the sequence are;
{29,9,-11,-31,...};
The first term of the sequence is
[tex]a_1=29[/tex]
The common difference is
[tex]d = 9 - 29 = - 20[/tex]
The nth term is given by:
[tex]a_n=a_1+d(n-1)[/tex]
Substitute the values to obtain,
[tex]a_{n}=29 - 20(n-1)[/tex]
[tex]a_{n}=29 - 20n + 20[/tex]
[tex]a_{n}=49 - 20n[/tex]
The indicated term is
[tex]a_{32}=49 - 20(32)[/tex]
[tex]a_{32}=-591[/tex]
