Sum of all natural numbers from100to300 which are divisible by 4and 5 is

If is a number that is both divisible by 4 and 5, then

4 and 5 are coprime, so we can use the Chinese remainder theorem to solve this system and find that is a solution to the system, where is any integer. Simply put, any multiple of 20 fits the bill.

Now, there are 11 numbers between 100 and 300 that are divisible by 20 (100, 120, 140, and so on). We have when , so the sum we want to compute is

An arithmetic sequence is a sequence where the difference between any two consecutive terms is a constant.

The constant between two consecutive terms is called the common difference.

The common difference is the number added to any one term of an arithmetic sequence that generates the subsequent term.

The terms of an arithmetic sequence can be found by beginning with the initial term and adding the common difference repeatedly.

Step-by-step explanation: