The average of the squares of the first 10 natural numbers is A. If each number is doubled first, and then squared, what is the new average?
Show answer & explanation
Correct answer: C
Explanation
Given:
First 10 natural numbers = 1, 2, 3,..., 10
Formula:
Sum of squares of the first n natural numbers = n(n+1)(2n+1) / 6
n = 10
Sum = 10 × 11 × 21 / 6 = 385
Average A = 385 / 10 = 38.5
New number = 2n
New square = (2n)² = 4n²
New average = 4A
= 4 × 38.5
= 154