To determine the $n$th term of the sequence $1, 5, 9, 13$, we can utilize the formula $4n - 3$.

This sequence is classified as an arithmetic sequence, characterized by a constant difference between consecutive terms. To find the $n$th term, we first need to establish the common difference. By calculating the difference between the second term and the first term, specifically $5 - 1$, we discover that the common difference is $4$. This indicates that each term is $4$ greater than the preceding term.

Next, we seek a formula that accurately represents the $n$th term of this sequence. The general formula for the $n$th term of an arithmetic sequence is given by:

$a + (n-1)d$

where $a$ represents the first term, and $d$ denotes the common difference. In our case, the first term $a$ is $1$, and the common difference $d$ is $4$. Substituting these values into the formula yields:

$\text{nth term} = 1 + (n-1) \times 4$

Now, let’s simplify this expression:

$\text{nth term} = 1 + 4n - 4$ $\text{nth term} = 4n - 3$

Consequently, the $n$th term of the sequence $1, 5, 9, 13$ can be expressed by the formula $4n - 3$. This formula enables you to calculate any term in the sequence by plugging in the desired position of the term ($n$) into the equation.

For instance, to find the $3$rd term, substitute $n = 3$ into the formula:

$\text{3rd term} = 4 \times 3 - 3 = 12 - 3 = 9$

This calculation confirms that the formula accurately represents the given sequence.