Part \( B \) Which of the following expressions can be used to lind the nith term in the patterm? A. \( 3(n-1) \) B. \( 3+5(n-1) \) C. \( 3+(n-1)+5 \) D. \( 3(n-1)+5 \)

To find the \( n \)-th term of a pattern, we need to analyze the given expressions and determine which one correctly represents the \( n \)-th term. Let's break down each option: A. \( 3(n-1) \) This expression suggests that the \( n \)-th term is a multiple of 3, but it does not account for a starting value or an increment. B. \( 3 + 5(n-1) \) This expression starts with 3 and adds increments of 5 for each term after the first. This is a common form for an arithmetic sequence. C. \( 3 + (n-1) + 5 \) This expression simplifies to \( 3 + 5 + (n-1) = 8 + (n-1) \), which does not clearly represent a consistent pattern. D. \( 3(n-1) + 5 \) This expression suggests that the \( n \)-th term starts with 5 and adds multiples of 3 for each term after the first. Now, let's analyze the expressions that are likely to represent an arithmetic sequence, which typically has the form \( a + (n-1)d \), where \( a \) is the first term and \( d \) is the common difference. From the analysis, option B \( 3 + 5(n-1) \) fits the form of an arithmetic sequence, where: - The first term \( a = 3 \) - The common difference \( d = 5 \) Thus, the correct expression to find the \( n \)-th term in the pattern is: **B. \( 3 + 5(n-1) \)**