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Write a general term a, for the following sequence. Assume that n begins with 1.

5 + 1/5, 5 -1/6, 5 + 1/7, 5 -1/8, ...........

The general term for the given sequence is an =

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Final answer:

The general term for the given sequence is an = 5 + (-1)^(n+1) / (4 + n). To find the general term, we notice that the sequence alternates between adding and subtracting a fraction. The signs of the fractions follow the pattern: +, -, +, -, ... This pattern can be represented by (-1)^(n+1), where n is the position of the term in the sequence. The denominators of the fractions follow the pattern: 5, 6, 7, 8, ... This pattern can be represented by (4 + n), where n is the position of the term in the sequence. Therefore, the general term is 5 + (-1)^(n+1) / (4 + n).

Step-by-step explanation:

The general term for the given sequence is an = 5 + (-1)^(n+1) / (4 + n).

To find the general term, we notice that the sequence alternates between adding and subtracting a fraction. The signs of the fractions follow the pattern: +, -, +, -, ... This pattern can be represented by (-1)^(n+1), where n is the position of the term in the sequence. The denominators of the fractions follow the pattern: 5, 6, 7, 8, ... This pattern can be represented by (4 + n), where n is the position of the term in the sequence. Therefore, the general term is 5 + (-1)^(n+1) / (4 + n).

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