Genus of a multiplicative sequence

Ok kiddo, have you ever heard of a sequence? It's like when you count in order from one to ten or twenty. Now, a multiplicative sequence is a special kind of sequence where each number is the product of the previous number and a fixed number. It's like when you count by twos: 2, 4, 6, 8, 10.

Now, every multiplicative sequence belongs to a group called a genus. Think of a genus as a family of sequences that are sort of like each other. Just like how you might have a family of cats, and all the cats have similar fur or eyes.

When we say a sequence belongs to a genus, we mean it has certain properties that are shared by all the other sequences in that genus. For example, some sequences might have the property that every number in the sequence is a perfect square (like 1, 4, 9, 16...). That would be one genus. Another genus might be all the sequences where every number is a multiple of 3 (like 3, 6, 9, 12...).

So, when we talk about the genus of a multiplicative sequence, we mean the family of sequences that share some common property or properties. We can sometimes tell what the genus is just by looking at the sequence and seeing what patterns or properties it has. It's like how you can tell two cats are related because they have the same kind of ears or tail.

I hope that helps you understand what a genus of a multiplicative sequence is, and how it's like a family of sequences that are similar in some way.