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In mathematics, a sequence is a set of numbers in a specific order. Each number in the sequence is known as a term. To describe each member of the sequence, we often use a general formula. This formula lets us find any term in the sequence by substituting different values of "n". For the sequence given in the exercise, the general term is \(a_n = \frac{2^n}{2^{n+1}}\). Here, the formula describes how each term is related to its position number, \(n\), in the sequence.
By replacing \(n\) with any natural number, we can find that term in the sequence. This relationship holds the pattern beneath the sequence, allowing us to more deeply understand or predict other terms.

Calculating terms in a sequence involves simple arithmetic operations. Starting with our general formula \(a_n = \frac{2^n}{2^{n+1}}\), we can easily find each sequence term through substitution and arithmetic steps.

• First, substitute \(n = 1\) to find the first term: \(a_1 = \frac{2^1}{2^{1+1}} = \frac{2}{4} = \frac{1}{2}\).
• Next, for the second term, substitute \(n = 2\): \(a_2 = \frac{2^2}{2^{3}} = \frac{4}{8} = \frac{1}{2}\).
• Continue this pattern for the third and fourth terms by using \(n = 3\) and \(n = 4\) respectively, calculating \(a_3 = \frac{8}{16} = \frac{1}{2}\) and \(a_4 = \frac{16}{32} = \frac{1}{2}\).

Through simple substitution and division, we uncover that each term equals \(\frac{1}{2}\). This consistent result underlines the sequence's uniformity.

Understanding exponent rules is vital when working with powers of numbers, especially in sequences. An exponent tells us how many times to multiply a number by itself. In the given formula \(\frac{2^n}{2^{n+1}}\), we frequently use these rules:

**Rule of Division of Exponents:** When dividing like bases, subtract the exponent in the denominator from the exponent in the numerator. For example, \(\frac{2^n}{2^{n+1}}\) simplifies to \(2^{n-(n+1)} = 2^{-1}\), which equals \(\frac{1}{2}\).

This rule allows us to simplify the sequence term easily, illustrating how knowing these rules can simplify complex-looking expressions into manageable calculations. By mastering exponent laws, we can tackle many algebraic problems with confidence.