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A random variable is a variable which can take different values and the values that it takes depends on some probability distribution rather than a deterministic rule. A random process is a process which can be in a number of different states and the transition from one state to another is random.
It is a sequence of numbers. That is all. The sequence could be arithmetic, geometric, harmonic, exponential or be defined by a rule that does not fit into any of these categories. It could even be random.
A sequence of numbers normally follows some rule (unless it is a random sequence) and no rule can be inferred from a single number, however, I can still invent one. My nomination is 984,339.79 as your next number.
It is an ordered set of elements. These elements may or may not be numbers, there may or may not be a defining rule - for example a sequence of random numbers.
The word random is used to describe a lack of pattern or organisation in behaviour. It may have very specific technical meanings in mathematics / statistics however. In math the term random usually means not able to be predicted or happening by chance. It implies a lack of order. In statistics we use the term random variable to mean a rule that applies a numerical outcome to each event in a sample space. More generally in statistics randomness means a lack of correlation or a lack of bias.