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Immediately springing to mind, geometric progression is used in accountancy in finding the Net Present Value of projects (specifically, the value of money each year based on the discount factor). It is also used in annuities, working out monthly repayments of loans and values of investments - compound interest is a geometric progression.
Airthmetic Progression
The history of arithmetic progression started with Euler. Later is was refined by Dirichlet which led to his theory of arithmetic progression.
A single number, such as 38978567796588 does not constitute a progression.
Progression Towards Evil was created in 1998.