The average of first ‘n’ natural numbers is 243. What is the average of the first ‘3n’ natural numbers?
As we know,
Sum of n natural numbers = n(n + 1)/2
⇒ Average of n natural numbers = (n + 1)/2
Given, Average of n natural numbers = 243
⇒ (n + 1)/2 = 243
⇒ n + 1 = 486
⇒ n = 486 – 1 = 485
⇒ 3n = 3(485) = 1455
∴ Average of 3n natural numbers = (1455 + 1)/2 = 1456/2 = 728