Find the difference between the average of the cube of the first 5 natural numbers and the average of the square of the first 5 natural numbers.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 34.
We know that,
The average of the cube of the first n natural numbers = n(n + 1)2/4
The average of the square of the first n natural numbers = (n + 1)(2n + 1)/6
Given that, the first (n = 5) natural numbers
The average of the cube of the first 5 natural numbers = 5 × (5 + 1)2/4
⇒ 5 × 9 = 45.........(1)
The average of the square of the first n natural numbers = (5 + 1)(2 × 5 + 1)/6
⇒ 6 × 11/6 = 11 ................(2)
The difference between equation (1) and (2)
⇒ 45 - 11 = 34
Hence, the required value is 34