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Difference between Sequence and Progression

A sequence is a set of numbers in a specific order such that you can predict the next number by a specific logic. For example, the following set of prime numbers:
2, 3, 5, 7...
is a sequence, because
• it is a set of numbers
• separated by commas
• in order of a specific logic (numbers are prime)
On the other hand, a progression is a sequence of numbers which has a specific mathematical formula. That is, you can predict the next term of a progression by the help of a formula, but you can't always have a formula to predict the next number of a sequence.

The set of prime numbers is a perfect example to differentiate between sequences and progressions; It is no doubt that the set of prime numbers is a sequence, but it is not a progression because there is no specific formula to predict the next prime number.