FHS Quarantine Math Academy - Sequences, Series and Probability

FHS Quarantine Math Academy

Sequences, Series and Probability

Below you will find a collection of videos that help teach the material taught in this unit. This includes anything and everything to do with sequences, series and probability! If you have any questions about the material you see, you can use this link to submit a question to a FHS math teacher.

Sequences intro | Algebra (video) | Khan AcademySequences are ordered lists of numbers (called "terms"), like 2,5,8. Some sequences follow a specific pattern that can be used to extend them indefinitely. For example, 2,5,8 follows the pattern "add 3," and now we can continue the sequence. Sequences can have formulas that tell us how to find any term in the sequence. For example, 2,5,8,... can be represented by the formula 2+3(n-1).

explicit and recursive formulas

Intro to arithmetic sequences | Algebra (video) | Khan AcademySal introduces arithmetic sequences and their main features, the initial term and the common difference. He gives various examples of such sequences, defined explicitly and recursively.

intro to arithmetic sequences

Explicit & recursive formulas for geometric sequences (video) | Khan AcademySal finds an explicit formula of a geometric sequence given the first few terms of the sequences. Then he explores equivalent forms the explicit formula and finds the corresponding recursive formula.

intro to geometric sequences

using sigma notation

Convergent & divergent geometric series (with manipulation) (video) | Khan AcademySal looks at examples of three infinite geometric series and determines if each of them converges or diverges. To do that, he needs to manipulate the expressions to find the common ratio.

convergent and divergent geometric series

part 1

Worked example: convergent geometric series (video) | Khan AcademySal evaluates the infinite geometric series 8+8/3+8/9+... Because the common ratio's absolute value is less than 1, the series converges to a finite number.

convergent and divergent geometric series

part 2

sum of an infinitive geometric series

sum of a finite geometric series

sum of a finite arithmetic series

the binomial theorem

pascal's triangle

binomial expansions

Part 1

Expanding binomials w/o Pascal's triangle (video) | Khan AcademySal gives a "trick" for expanding large powers of binomials, without using Pascal's triangle.

binomial expansions

Part 2

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