* What is the average of the first n positive even numbers?
ME COOL KID PINEAPPLE
To find the average of the first n positive even numbers, we need to follow these steps:
1. Understand the problem: We want to calculate the average of the first n positive even numbers. Given any value of n, we need to determine the average.
2. Find the formula for the nth positive even number: We know that even numbers are multiples of 2. The formula to find the nth positive even number is 2n.
3. Calculate the sum of the first n positive even numbers: To find the sum, we need to add up the first n positive even numbers. The formula for the sum of an arithmetic series is S = (n/2) * (a + b), where a is the first term and b is the last term. In this case, a = 2 and b = 2n.
S = (n/2) * (2 + 2n) = n * (1 + n)
4. Calculate the average: To find the average, we divide the sum by the total count, which is n.
Average = S/n = n * (1 + n) / n = 1 + n
Therefore, the average of the first n positive even numbers is 1 + n.
For example, if we want to find the average of the first 5 positive even numbers, we substitute n = 5 into the formula:
Average = 1 + n = 1 + 5 = 6
So the average of the first 5 positive even numbers is 6.
my wife took all the kinds i will jump of a bridge
pair them up
2,2n
4,2n-2
6,2n-4
...
What is the average of each pair?
Or, consider their sum:
2+4+...+2n
= 2(1+2+...+n)
= 2*n(n+1)/2
= n(n+1)
So, what is the average of that sum?