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?
The nth term of the sequence is given by 4n + 5.
In an arithmetic sequence, the nth term can be expressed as ( a + (n-1)d ), where ( a ) is the first term and ( d ) is the common difference. Given that the 2nd term equals T and the 6th term equals LS, we can derive the formula for the nth term, leading to the conclusion that it simplifies to 4n + 5.
This option implies a common difference of 2 and an adjusted first term. However, substituting values for T and LS based on the sequence properties does not yield consistent results with the given terms in the problem. Therefore, this expression cannot represent the nth term accurately.
While this option has a linear form, it suggests a common difference of 2 and a starting point that does not align with the relations given between the 2nd and 6th terms. This choice fails to meet the criteria established by T and LS, confirming it is incorrect for the nth term.
This choice indicates a common difference of 3, which does not match the arithmetic properties linking the 2nd and 6th terms. Evaluating the sequence with this expression leads to discrepancies when attempting to equate it to T and LS, thus making it an invalid option.
This selection proposes a common difference of 4, which overshoots the required difference observed between the terms T and LS. Testing this formula against the sequence properties reveals inconsistencies, confirming that it cannot represent the nth term accurately.
This option correctly reflects the arithmetic sequence's behavior based on the established differences between the terms. By substituting the known values for T and LS into this expression, it holds true, demonstrating that this is the correct formula for the nth term.
The nth term of an arithmetic sequence can be derived from the relationships between its terms. In this case, the consistent application of the arithmetic sequence formula leads us to identify 4n + 5 as the valid nth term, as it aligns perfectly with the conditions set forth by the 2nd and 6th terms, T and LS.
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