The start of a sequence of patterns made from sticks is shown below. The same number of sticks is added each time.

What is the rule for the number of sticks in the $n^{\text {th }}$ pattern?
Sticks in ${ }^{\text {th }}$ pattern:

Step 1 ：\(\text{Let } a_n \text{ be the number of sticks in the } n^{\text{th}} \text{ pattern.}\)

Step 2 ：\(\text{Notice that the difference between consecutive terms is constant and equal to } 3.\)

Step 3 ：\(\text{Thus, we can write the sequence as an arithmetic sequence with the first term } a_1 = 1 \text{ and common difference } d = 3.\)

Step 4 ：\(\text{The formula for the } n^{\text{th}} \text{ term of an arithmetic sequence is } a_n = a_1 + (n - 1)d.\)

Step 5 ：\(\text{Substitute the values } a_1 = 1 \text{ and } d = 3 \text{ into the formula: }\)

Step 6 ：\(a_n = 1 + (n - 1)3\)

Step 7 ：\(a_n = 1 + 3n - 3\)

Step 8 ：\(\boxed{a_n = 3n - 2}\)