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Sequences
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Calculus
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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 co...
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 chewing...
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 pickmeup in the morning, "One. One large coffee. Ha.Ha.Ha." Why would we begin counting se...
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 each term is the same. A geometric sequence is a lot like an arithmetic se...
Comparing Arithmetic and Geometric Sequences
When we were young, we were all taught to addition and subtraction first. Then we endured the endless multiplication tables, and we learned division is multiplications 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 notsougly 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 are comfortable with limits, and let's...
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 road....
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