How do you find the nth term of 1, 5, 9, 13?

To find the nth term of the sequence 1, 5, 9, 13, use the formula 4n - 3.

This sequence is an example of an arithmetic sequence, where each term increases by a constant difference. To identify the nth term, we first need to determine the common difference. By subtracting the first term from the second term (5 - 1), we find that the common difference is 4. This means that each term is 4 more than the previous one.

Next, we need to find a formula that represents the nth term of the sequence. The general form of the nth term of an arithmetic sequence is given by \(a + (n-1)d\), where \(a\) is the first term and \(d\) is the common difference. For our sequence, the first term \(a\) is 1, and the common difference \(d\) is 4. Substituting these values into the formula, we get:

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

Simplifying this expression:

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

Therefore, the nth term of the sequence 1, 5, 9, 13 is given by the formula \(4n - 3\). This formula allows you to find any term in the sequence by substituting the position of the term (n) into the formula. For example, to find the 3rd term, substitute \(n = 3\):

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

This confirms that the formula works for the given sequence.