general term for the sequence: 1/4, 2/13, 1/9, 2/23
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Answer:
To find the general term for the given sequence, let's analyze the pattern:
1/4, 2/13, 1/9, 2/23
Looking at the numerators, we can see that they alternate between 1 and 2. The denominators, on the other hand, follow a pattern where they increase by 9 and then by 14.
Based on this observation, we can express the general term as follows:
If the index (n) is odd:
tn = 1 / (4 + 9 * ((n - 1) / 2))
If the index (n) is even:
tn = 2 / (13 + 14 * ((n - 2) / 2))
In both cases, we use integer division ((n - 1) / 2 or (n - 2) / 2) to account for the alternating pattern.
Therefore, the general term for the sequence is given by:
Therefore, the general term for the sequence is given by:tn = 1 / (4 + 9 * ((n - 1) / 2)) if n is odd
Therefore, the general term for the sequence is given by:tn = 1 / (4 + 9 * ((n - 1) / 2)) if n is oddtn = 2 / (13 + 14 * ((n - 2) / 2)) if n is even
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