What is the greatest positive integer that must divide the sum of the first ten terms of any arithmetic sequence whose terms are positive integers?
Solution:
The first 10 terms of an arithmetic sequence can be represented as, where is the first term and is the constant difference between each consecutive term. So, the sum of all of these terms will include and, which equals. As a result, the sum of all the terms is and the greatest number we can factor out is, where we end up with 5(2x+9c). or 5
