The Common Progression Problem

Algebra Level 3

I have 2 arithmetic progressions: \[ \begin{cases} 16,21,26,31, \ldots \\ 21,25,29,33, \ldots \end{cases} \] The number 21 appears in both of these progressions.
There are also other numbers that appear in both of these 2 progressions!

What is the sum of the first 100 common terms of these 2 progressions?

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