Generalized arithmetic progression
Imagine you have a group of numbers that are all related in a special way. They all increase by the same amount each time. For example, you might have the numbers 1, 3, 5, 7, 9, where each number is 2 more than the one before it. We call this relationship "arithmetic progression."
Now imagine that instead of starting at 1 and adding 2 each time, you can start at any number and still add the same amount each time. For example, you might start at 4 and add 3 each time to get 4, 7, 10, 13, 16. This is still an arithmetic progression, but it's not as specific as the first one because it can start at any number.
This kind of arithmetic progression where the starting number and the amount added each time can be any number is called "generalized arithmetic progression." It's like a flexible version of the usual arithmetic progression.
Now imagine that instead of starting at 1 and adding 2 each time, you can start at any number and still add the same amount each time. For example, you might start at 4 and add 3 each time to get 4, 7, 10, 13, 16. This is still an arithmetic progression, but it's not as specific as the first one because it can start at any number.
This kind of arithmetic progression where the starting number and the amount added each time can be any number is called "generalized arithmetic progression." It's like a flexible version of the usual arithmetic progression.
Related topics others have asked about: