How do you find the average of cubes of natural numbers?

Mean of any given set of data is determined by dividing the sum of the given data from the number of data present in that set. It gives the average value of that set of data. Mean of cubes of the first 15 natural numbers can be calculated by dividing the sum of first 15 natural numbers from 15.

What is the average of natural numbers from 1 to 25?

As known, Let the Sum of n natural numbers be S. ∴ Average of first 25 natural numbers is 13. ∴ Average of first 25 natural numbers is 13.

What is the average of cubes of first 9 natural numbers?

So, the average of the cubes of first 9 natural numbers is 225.

What is the average of square of the natural number from 1 to 41?

So, The average of square of the natural number from 1 to 41 is 581.

How do you find the average of first 100 natural numbers?

The average of first 100 natural numbers is how much times of average of next 100 natural numbers

1. sum of 1st n numbers is n(n+1)/2.
2. ” ” ” 100 ‘” ” ” ” “100(101)/2=5050.
3. average of 1st 100 numbers is 5050/100=50.5.
4. Similarly sum of next 100 numbers is 15050.
5. average of these numbers is 15050/100=150.0.

How do you find the average of first 50 natural numbers?

Detailed Solution

1. Shortcut Trick. Average of n consecutive number (for odd value of n) = [middle term + (middle + 1) term] ÷ 2.
2. Detailed Solution:
3. Given: First 50 natural numbers.
4. Calculation: First 50 natural numbers are 1, 2, 3,…….
5. ∴ The average of first 50 natural numbers is 25.5.
6. Shortcut Trick.

What is the sum of cubes of first 8 natural numbers?

The sum of cubes of the first 8 natural numbers is 1296. Let us look at how we got the answer. Sum of cubes of 8 natural numbers = [82 (8 + 1)2]/4 = (64 × 81)/4 = 1296.

What is the average of square of the natural number from 1 to 10?

first 10 natural numbers. ∴ The average of squares of first 10 natural numbers is 38.5.

How do you find the average of a square number?

The average of the square of Natural Number is calculated by adding all the squares up to n natural numbers and then dividing it by the number.

What is the average of cubes of first “n” natural numbers?

Average of cubes of first “n” even natural numbers = 2n (n +1) 2 12. Average of cubes of first “n” odd natural numbers = n (2n2 – 1) 13.

What is the average of 1 to n natural numbers?

Average of first ” n” natural numbers = 2. Average of first ” n” even numbers = ( n + 1 ) 3. Average of first ” n ” odd numbers = n 4. Average of consecutive numbers = 5. Average of 1 to “n” odd numbers = 6. Average of 1 to “n” even numbers = 7.

What are some examples of average numbers?

In this Exercise – 2 given formulas with examples for average of numbers like first “n “natural numbers , average of even numbers, average of odd numbers, average of constitutive numbers, Average of cubes of first ” n” natural, even, odd numbers … etc

What is the average of first n even and odd numbers?

Average of sum of square of first “n” even numbers = 9. Average of sum of square of first “n” odd numbers = 10. Average of cubes of first ” n” natural numbers = 11. Average of cubes of first “n” even natural numbers = 2n ( n +1) 2 12.