Sum-free sequence
Imagine you have a basket full of different colored balls. A sum-free sequence is like making a new list of some of those balls but with a special rule. The rule is that you can't add any two balls in the list together to get a third ball that's also in the list.
For example, if you have a list that goes like "blue, green, yellow, green," you can't add the two green balls together to get "yellow," because "yellow" is already in the list. So, this wouldn't be a sum-free sequence.
But if you made a list that goes like "red, green, blue," that's a sum-free sequence because no two of those balls can add up to be another ball in the list.
In math, when we talk about sequences, we usually use numbers instead of colored balls. But the concept is the same. A sum-free sequence is just a list of numbers where you can't add any two of them together to get a third number that's also in the list. This can be really useful for solving certain math problems!
For example, if you have a list that goes like "blue, green, yellow, green," you can't add the two green balls together to get "yellow," because "yellow" is already in the list. So, this wouldn't be a sum-free sequence.
But if you made a list that goes like "red, green, blue," that's a sum-free sequence because no two of those balls can add up to be another ball in the list.
In math, when we talk about sequences, we usually use numbers instead of colored balls. But the concept is the same. A sum-free sequence is just a list of numbers where you can't add any two of them together to get a third number that's also in the list. This can be really useful for solving certain math problems!