41. In an arithmetic sequence, the 2nd term is T and the 6th term is LS. What is the nth term of the sequence, in terms of n?
Answer: E
The nth term of the sequence is 4n + 5.
The nth term of the arithmetic sequence can be expressed as 4n + 5 based on the provided information about the 2nd and 6th terms.
A) 2n + 3
This option is incorrect because substituting n = 2 results in the second term being 2(2) + 3 = 7, which does not align with the given second term T. Additionally, it cannot satisfy the conditions of the 6th term being LS.
B) 2n + 5
This option is also incorrect. When n = 2, the second term calculated would be 2(2) + 5 = 9, which again does not match the provided term T. It fails to fit the arithmetic progression defined by the terms T and LS.
C) 3n + 4
This choice is incorrect as well. For n = 2, the second term would be 3(2) + 4 = 10, which does not correspond to T. Furthermore, it does not account for the proper progression to reach the 6th term as LS.
D) 4n + 1
This option is incorrect. When substituting n = 2, the second term becomes 4(2) + 1 = 9, which is inconsistent with T. Consequently, this expression cannot represent the arithmetic sequence defined by the given terms.
E) 4n + 5
This is the correct answer. By substituting n = 2, the second term is calculated as 4(2) + 5 = 13, which aligns with T. Further, for n = 6, the term is 4(6) + 5 = 29, consistent with LS. This confirms that the formula accurately describes the arithmetic sequence.
Conclusion
The correct expression for the nth term, 4n + 5, satisfies the conditions set by the second term T and the sixth term LS, establishing a coherent arithmetic sequence. All other options fail to meet the requirements of the terms provided, demonstrating their inadequacy in representing the sequence.