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Consider the arithmetic sequences:

$1998, 2005, 2012, ...$ and

$1996, 2005, 2014, ...$

$1996, 2005, 2014, ...$

Which is the next number after $2005$ that appears in both sequences?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

*This problem is taken from the UKMT Mathematical Challenges.*