What is the pattern for n times 3 plus 1

Given the way the problem is written in your worksheet (attachment):

"n x 3 +1 " ; you would write:

"nine times three plus 1"  as:

(n*3) + 1 ; (Using the order of operations: BE MD AS; which stands for:
                                                                 "Be excused, my dear Aunt Sally";
                                                                    or other variant phrase);

Using this "order of operations" rules; we know that "multiplication" comes BEFORE "addition"; as such:

Given: "n * 3 + 1"; we can write: 

(n*3) + 1 ; with the parentheses as an emphasis that this                                                   "multiplication" component comes first.

By convention, when a variable has a coefficient other than "1", we usually write the term with the coefficient coming before the variable.

So, we can rewrite:

(n*3) + 1  ;  as:

(3*n) + 1 .

By convention; if we have a coefficient multiplied by a variable (symbolized with an "alphabet letter"), we simply write that coefficent, followed by the [variable symbolized with an "alphabet letter"]. By convention, the implication is that multiplication is inherent in these circumstances.

So, "(3*n)" can be rewritten as "3n"; 

And the term for the "pattern" (which is not an 'equation'); is:

3n + 1

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b. 2/3