Algebra 2: Resources and Extra Practice - 7.01 Arithmetic Sequences and Series

Algebra 2: Resources and Extra Practice

7.01 Arithmetic Sequences and Series

Essential Question:

How can an expression or process be determined for an arithmetic sequence?
What functions combine to create an explicit formula for arithmetic sequences?
What possible restrictions exist on domains and ranges of arithmetic sequences?
How can an expression or process be determined for an arithmetic series?

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Khan Academy Resources

Sequences introSequences 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).

Intro to arithmetic sequencesSal 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.

Using arithmetic sequences formulasSal finds terms of arithmetic sequences using their explicit and recursive formulas.

Worked example: using recursive formula for arithmetic sequenceExample finding the 4th term in a recursively defined arithmetic sequence.

Arithmetic series introSal explains the formula for the sum of a finite arithmetic series

Worked example: arithmetic series (sum expression)Sal evaluates the arithmetic sum (-50)+(-44)+(-38)+...+2044. He does that by finding the number of terms and using the arithmetic series formula (a₁+aₙ)*n/2.

Worked example: arithmetic series (recursive formula)Sal evaluates the sum of the first 650 terms in the sequence defined recursively as {aᵢ=aᵢ₋₁+11, a₁=4}. He does that by finding the 650th term and using the arithmetic series formula (a₁+aₙ)*n/2.

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