1. \( A(n) \) is the value of the \( n \)th term of the sequence \( 26,39,52,65,78 \). Is the domain of the function continuous or discrete? Explain. the domain of the function is continuous because the range has a constatnt rate of 13 and the domain is your \( x \) value and will go on continuously

Let's analyze the sequence \( A(n) = 26, 39, 52, 65, 78 \) and determine the nature of its domain. 1. **Identify the Sequence**: The sequence consists of the terms \( 26, 39, 52, 65, 78 \). We can observe that each term increases by a constant value of \( 13 \). 2. **Define the Function**: The \( n \)th term of the sequence can be expressed as: \[ A(n) = 26 + 13(n - 1) \] This formula indicates that for each integer \( n \), we can find a corresponding term in the sequence. 3. **Determine the Domain**: The domain of the function \( A(n) \) consists of the values of \( n \) for which the function is defined. In this case, \( n \) takes on positive integer values (1, 2, 3, ...). 4. **Continuous vs. Discrete**: - A **discrete** domain consists of distinct, separate values (like integers). - A **continuous** domain includes all values within a range (like real numbers). Since \( n \) can only take on positive integer values, the domain of the function \( A(n) \) is discrete. ### Conclusion: The domain of the function \( A(n) \) is discrete because it consists of specific integer values (1, 2, 3, ...), rather than a continuous range of values. The statement that the domain is continuous is incorrect; it is the range that has a constant rate of change, but the domain itself is not continuous.