In this quiz we explore various sequences, which not only make for fun puzzles but are central to algebra.

Could you describe this pattern well enough that someone could reproduce it without having seen it?

How many squares will be in Step 99?

Does column 15 have more stars or squares?

Hint: notice that each horizontal row has its own pattern.

**empty squares** does Figure 10 have?

$s = 1$ has one unit cube. Assuming the pattern continues as shown, **how many unit cubes will $s = 4$ have?**

(Note: We want all cubes being used, not just that are visible from the starting angle.)

Extending patterns as we've done in the preceding questions is a foundational algebra skill.

While we can solve many problems like these in a straightforward manner, the use of variables, equations, and algebraic concepts unlocks a variety of additional problems. We will finish our introduction with a problem that benefits from the careful application of variables.

Jill is arranging tables for a party that will be placed in one long row, end to end. Each side of each table can seat one person.

Which table shape **cannot** seat exactly 50 people, regardless of the number of tables used?