The average of the integers from 25 to 41 is 33.
Calculating the Average
According to the provided reference, the average of a set of numbers is calculated by dividing the sum of the numbers by the count of numbers.
Step-by-Step Calculation
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Identify the Integers: The integers from 25 to 41 are: 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, and 41.
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Count the Integers: There are 17 integers in this sequence.
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Sum the Integers: The sum of these integers is 561.
- Sum Calculation: 25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 = 561
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Calculate the Average: Divide the sum (561) by the count of integers (17): 561 / 17 = 33.
- Average Formula: Average = (Sum of integers) / (Number of integers)
- Calculation: Average = 561 / 17 = 33
Shortcut using Arithmetic Sequence Property
In an arithmetic sequence (where the difference between consecutive terms is constant, like the sequence of integers), the average is also the mean (middle) of the first and last terms:
- Average = (First term + Last term) / 2
- Average = (25 + 41) / 2
- Average = 66 / 2
- Average = 33
Table Representation
| Step | Calculation | Result |
|---|---|---|
| Sum of Integers | 25 + 26 + ... + 41 | 561 |
| Number of Integers | Count from 25 to 41 | 17 |
| Average | 561 / 17 | 33 |
| Average Shortcut Method | (25 + 41) / 2 | 33 |
Therefore, the average of the integers from 25 to 41 is 33.
