The average of first 124 even numbers is
125
To find the average of the first 124 even numbers, we can use the formula for the average of the first n even numbers. The formula to find the n-th even number is given by:
2n
Thus, the first 124 even numbers are: 2, 4, 6, ..., 2 × 124.
The formula for the average of the first n natural numbers is:
Average = (Sum of n numbers) / n
The sum of the first n even numbers is:
Sum = 2 + 4 + 6 + ... + 2n = 2(1 + 2 + 3 + ... + n)
The sum of the first n natural numbers is given by:
Sum = n(n + 1)/2
Therefore, the sum of the first n even numbers is:
2 × n(n + 1)/2 = n(n + 1)
Substituting n = 124:
Sum = 124 × 125
Thus, the average of the first 124 even numbers is:
Average = (124 × 125) / 124
= 125
Therefore, the average of the first 124 even numbers is 125.
Important Questions from Average
The average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14 th number is excluded, then what is the average of remaining numbers? (correct to one decimal places)
24 students collected money for donation. The average contribution was Rs. 50. Later on, their teacher also contributed some money. Now the average contribution is Rs. 56. The teacher’s contribution is:
Out of 6 numbers, the sum of the first 5 numbers is 7 times the 6 th number. If their average is 136, then the 6 th number is:
The average of five numbers is 30. If one number is excluded, then average becomes 31. What is the excluded number?
The average weight of 49 students in a class is 39 kg. Seven of them whose average weight is 40 kg leave the class and other seven students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class?
