MI 4 Learning Targets Unit 1
Sequences and Series
Sequences
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Define a sequence
Given an explicit formula for a sequence, find several terms
Given a recursive formula for a sequence, find several terms
Given several terms of a sequence, find a formula
Determine if a sequence is arithmetic, geometric, harmonic, or none of these
Use knowledge of sequences in various applications
Series
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Define a series
Create a sequence of partial sums
Use sigma notation, both to write individual terms of a series and to express a series with
this notation
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Simplify and evaluate
n
 P(k ) where P(k ) is a polynomial of degree 3 or less
k 1
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Use knowledge of series in various applications
Arithmetic, Geometric, and Harmonic Sequences
 Find the formula for the nth term, both explicit and recursive
 Find the arithmetic, geometric, and the harmonic means
Arithmetic and Geometric Series
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Use formulas to find the sum of n terms of an arithmetic or geometric series
Determine if an infinite geometric series converges
Find the sum of an infinite, convergent geometric series
Convert a repeating decimal to a fraction using the properties of series
Notation
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Reading and using subscripts
Notation for sequences – { }
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Sigma notation –
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Expressing sequences and series recursively and explicitly with correct notation
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F13
MI 4 Learning Targets Unit 1
Sequences and Series
Vocabulary – terms we will use in this unit
sequence
series
geometric, arithmetic, harmonic sequence
geometric, arithmetic, harmonic mean
convergent sequences and series
divergent sequences and series
sequence of partial sums
limit of a sequence
explicit formula
recursive formula
common difference
common ratio
factorial
telescoping series
alternating series
F13