What will be the average of even numbers between 11 to 63. (Firstno la...
The formula says the total sum starting from 0 not by a specific one so you failed
What will be the average of even numbers between 11 to 63. (Firstno la...
Calculating the average of even numbers between 11 to 63:
To find the average of a set of numbers, you need to sum all the numbers together and then divide by the count of numbers in the set. In this case, we are looking for the average of even numbers between 11 and 63.
Finding the count of even numbers:
To determine the count of even numbers between 11 and 63, we can observe that the first even number in this range is 12 and the last even number is 62. So, there are (62 - 12)/2 + 1 = 51 even numbers.
Summing the even numbers:
To calculate the sum of even numbers, we can use the formula for the sum of an arithmetic series, which is Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term.
In this case, the first term is 12 and the last term is 62. So, the sum of the even numbers is (51/2)(12 + 62) = 51 * 74 = 3774.
Calculating the average:
To find the average, we divide the sum of the even numbers by the count of even numbers:
Average = Sum / Count = 3774 / 51 = 74.
Therefore, the average of even numbers between 11 and 63 is 74.
Explanation of the formula in the IAF book:
The formula mentioned in the IAF book, which states that the average of consecutive even numbers up to n is n/2, is applicable when you have a consecutive sequence of even numbers starting from 2. In that case, the count of even numbers would be n/2, and the sum of the even numbers would be (n/2)(2 + n).
However, in the given problem, we have a range of even numbers between 11 and 63, which is not a consecutive sequence starting from 2. Therefore, we cannot apply the formula directly in this scenario.
It's important to understand the context and conditions under which a formula can be used, as different situations may require different approaches. In this case, finding the count and sum of the even numbers between 11 and 63 and then calculating the average using those values gives us the correct result.
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