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