# Sequences Exercises

#### Defining Sequences and Evaluating Terms

Let's imagine, instead of numbers, we have a sequence of animals. The sequence begins with three animals: green tap dancing elephant, purple singing cockatoo, and orange quarterback tiger. We cou...

#### Patterns

Evaluating terms of a sequence, given the formula, isn't so bad. Going the other way around is a little trickier. It can be a bit like juggling buzzing chainsaws while riding a unicycle and chewi...

#### Sequences Can Start at *n* = 0

Remember the Count from Sesame Street? Now a little bit older and with a few gray hairs, he needs a good pick-me-up in the morning, "One. One large coffee. Ha.Ha.Ha." Why would we begin counting...

#### Arithmetic Sequences

An arithmetic sequence is a sequence where the step from one term to the next is constant. That is, you always add the same thing to get from one term to the next. An arithmetic sequence is like go...

#### Geometric Sequences

We already know that an arithmetic sequence is one where the difference between successive terms is constant. The distance from each term is the same. A geometric sequence is a lot like an arithm...

#### Comparing Arithmetic and Geometric Sequences

When we were young, we were all taught addition and subtraction first. Then we endured the endless multiplication tables, and we learned division is multiplication's partner operation. We did the...

#### Visualizing Sequences

For those who like pictures better than formulas, we can visualize sequences on number lines and on graphs. For those who like Kit Kats, we can visualize a giant Kit Kat bar. Either way, creating a...

#### Convergence and Divergence of Sequences

Now calculus rears its not-so-ugly head. Sequences are like bulls at a rodeo waiting to be lassoed, but the divergent ones can't be caught. Let's make sure we're comfortable with limits, and let'...

#### Word Problems

Sequences, especially arithmetic and geometric ones, are good for word problems. Sequence story problems come in two main flavors. If these flavors were ice cream, they'd be vanilla and rocky roa...