Sum of natural numbers divisible by 11 between 100 to 1000

To find the sum of natural numbers between 100 and 1000 which are divisible by 11, we need to follow the below steps:

Step 1: Find the first natural number divisible by 11 between 100 and 1000.

Step 2: Find the last natural number divisible by 11 between 100 and 1000.

Step 3: Find the total number of natural numbers between the first and last natural numbers divisible by 11.

Step 4: Find the sum of all the natural numbers between the first and last natural numbers divisible by 11.

Step 1: Find the first natural number divisible by 11 between 100 and 1000.

The first natural number divisible by 11 between 100 and 1000 is 110.

Step 2: Find the last natural number divisible by 11 between 100 and 1000.

The last natural number divisible by 11 between 100 and 1000 is 990.

Step 3: Find the total number of natural numbers between the first and last natural numbers divisible by 11.

To find the total number of natural numbers between 110 and 990 which are divisible by 11, we need to use the following formula:

Total Numbers = (Last Number - First Number)/Common Difference + 1

Here, First Number = 110, Last Number = 990 and Common Difference = 11

Total Numbers = (990 - 110)/11 + 1

Total Numbers = 81

Step 4: Find the sum of all the natural numbers between the first and last natural numbers divisible by 11.

To find the sum of all the natural numbers between 110 and 990 which are divisible by 11, we need to use the following formula:

Sum = (n/2)(first term + last term)

Here, n = 81, first term = 110 and last term = 990

Sum = (81/2)(110 + 990)

Sum = 44,550

Therefore, the sum of all the natural numbers between 100 and 1000 which are divisible by 11 is 44,550. Hence, the correct answer is option 'A'.