Mathematics

Mathematics

Problem

Determine if the number 1999 belongs to the sequence that begins with 7, 16, 25, 34, ...
Intuitive explanation

This is an arithmetic sequence problem—you need to recognize the pattern and test membership. Notice the sequence has a constant difference between consecutive terms; once you find that common difference dd, you can write a formula for the nn-th term. Then check whether 1999 fits that formula by solving for nn—if nn is a positive integer, 1999 is in the sequence; if not, it isn't.

Intuitive explanation

This is an arithmetic sequence problem—you need to recognize the pattern and test membership. Notice the sequence has a constant difference between consecutive terms; once you find that common difference dd, you can write a formula for the nn-th term. Then check whether 1999 fits that formula by solving for nn—if nn is a positive integer, 1999 is in the sequence; if not, it isn't.

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