A sequence {an} in which an+1 ……. an is the same number for all n ∈ N is called

A sequence $\{a_n\}$ in which $a_{n+1} = a_n$ for all $n \in \mathbb{N}$ is called a constant sequence.

In a constant sequence, every term in the sequence is equal to the same fixed number, say $c$. Therefore, the sequence can be represented as $a_n = c$ for all $n$. Constant sequences are an important concept in mathematics as they provide a simple form of sequences that do not change with $n$.

For example, if we define $c = 5$, the constant sequence would be $\{5, 5, 5, 5, \ldots\}$. These sequences are foundational in various areas of analysis and algebra.