# Sequences

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?

# Sequences

How many squares will be in Step 99?

# Sequences

Does column 15 have more stars or squares?

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

# Sequences

In each figure, squares are either empty or filled with a circle. How many empty squares does Figure 10 have?

# Sequences

Unit cubes are stacked to create a large cube of size $$10 \times 10 \times 10$$. The outside of the cube is then painted green. How many unit cubes will have exactly one face painted green?

# Sequences

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.

# Sequences

Jill is arranging tables for 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?

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