The question is slightly ambiguous. It could be interpreted in two ways: (1) What is the average of the number of odd numbers up to 100, or (2) What is the average value of the odd numbers up to 100? Let's address both interpretations.
Interpretation 1: Average of the number of odd numbers.
This interpretation doesn't make much sense mathematically. We're not averaging the number of odd numbers. This interpretation is disregarded.
Interpretation 2: Average value of odd numbers up to 100.
This is the more likely interpretation of the question. We want to find the average of all odd numbers from 1 to 99 (inclusive).
Solution:
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Identify the odd numbers: The odd numbers up to 100 are 1, 3, 5, 7, ..., 99.
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Recognize the arithmetic sequence: This is an arithmetic sequence with a common difference of 2.
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Use the average formula for arithmetic sequences: The average of an arithmetic sequence is simply the average of the first and last terms. The average = (First Term + Last Term) / 2.
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Calculate the average:
Average = (1 + 99) / 2 = 100 / 2 = 50
Therefore, the average of all odd numbers up to 100 is 50. As indicated by Testbook, the average of odd numbers from 1 to 100 is 50.
