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Arithmetic and Geometric Sequences

Arithmetic and Geometric Sequences

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Author: Justin Souza
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Standards:

CCSS.MATH.CONTENT.HSF.LE.A.1

Distinguish between situations that can be modeled with linear functions and with exponential functions.

CCSS.MATH.CONTENT.HSF.LE.A.1.A

Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

CCSS.MATH.CONTENT.HSF.LE.A.1.B

Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

CCSS.MATH.CONTENT.HSF.LE.A.1.C

Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

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Tutorial

Task

An arithmetic sequence increase by a common difference. For example the sequence (10, 15, 20, 25, ....) increases by 5. 

Students will be able to identify an arithmetic sequence, and create both a recursive and explicit expression using the sequence.

Recursive Expression is simple using the prior term to calculate the next.

It will always be in the form f(n) = f(n-1) + d.

This expression simple states that any function of term n equals the function of term n-1 plus the common difference.