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Find a general expression for the ( n )th term in the sequence

n = -1/6, -1/3, -3/8, -16/68, -25/96, -36/192, ........

1 Answer

3 votes

Final answer:

The question asks for a general expression for the n-th term of a sequence, but the given terms do not show a clear pattern to derive a formula. Additional information about how the terms are generated is necessary to establish a general expression.

Step-by-step explanation:

The sequence presented in the question appears to be of the form n = (negative numerator)/(denominator), where the numerator is the square of the index of the term and the denominator increases in a specific pattern. However, to derive a general formula for the n-th term of the sequence given in the question, we need more information about how the numerators and denominators are generated, as they do not follow an easily discernible pattern. Without a clear rule for the progression of the sequence, calculating the general expression for the n-th term is not feasible.

When analyzing sequences, it is crucial to identify the pattern in the terms. Often, the use of difference methods or recognizing arithmetic or geometric sequences helps to determine such patterns. Unfortunately, with the given information, we cannot determine a clear mathematical relationship between the terms provided. Therefore, a general expression for the n-th term cannot be given with the information provided.

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