What is the sum of all natural numbers between 300 and 500 divisible by 11?

The sum of all natural numbers between 300 and 500 that are divisible by 11 is 7227.

Let's break down how to arrive at this answer:

1. Identify the first and last numbers in the range divisible by 11:

   • The first number greater than 300 divisible by 11 is 308 (since 300 / 11 ≈ 27.27, we round up to 28 and multiply by 11: 28 * 11 = 308).
   • The last number less than 500 divisible by 11 is 495 (since 500 / 11 ≈ 45.45, we round down to 45 and multiply by 11: 45 * 11 = 495).

2. Form an arithmetic progression:

   • The numbers divisible by 11 between 300 and 500 form an arithmetic progression: 308, 319, 330, ..., 495.
   • The common difference (d) is 11.

3. Find the number of terms (n) in the arithmetic progression:

   • We use the formula: last term = first term + (n - 1) * common difference
   • 495 = 308 + (n - 1) * 11
   • 187 = (n - 1) * 11
   • 17 = n - 1
   • n = 18

4. Calculate the sum (S) of the arithmetic progression:

   • We use the formula: S = (n/2) * (first term + last term)
   • S = (18/2) * (308 + 495)
   • S = 9 * 803
   • S = 7227

Therefore, the sum of all natural numbers between 300 and 500 divisible by 11 is 7227.