7.5.1 Numerical Patterns

Compare your answer:

Things you may notice:

• The $x$-values increment by 1 as you move across the table.
• The $y$-values increase.
• All $y$-values are even and divisible by 4, 8, and 16.
• The $y$-values are all perfect squares.
• The successive differences between the $y$-values are growing.

Things you may wonder:

• Is there a rule for these numbers?
• Do the numbers represent the growth of a geometric pattern?
• Do the numbers represent a quadratic relationship?
• What is the next number in the table?