9.4 Notes.notebook
February 18, 2016
9.4 Arithmetic Series
Name: ______________________
Objectives: Students will be able to define arithmetic series and
find their sums.
Finite series: has a first and last term
Ex:
Infinite Series: continues without end
Ex:
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An ___________ _______ is a series whose terms form an
arithmetic sequence. When an arithmetic series has a finite
number of terms, we can use a formula to evaluate the sum. Let's
find out how our friend Gauss, a German mathematician,
discovered this formula.
1777-1855
The sum of the first n terms of an arithmetic series is given by
Sn =
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9.4 Notes.notebook
February 18, 2016
Examples Find the sum of the finite arithmetic series.
1.) 1 + 4 + 7 + ... + 31
2.) (-3) + (-6) + ... + (-30)
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A student has taken three math tests so far this semester. His
scores for the first tests were 75, 79 and 83.
a.) Suppose his test scores continue to improve at the same rate.
What will be his grade on the sixth (and final) test?
b.) What will his total score be for all six tests?
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9.4 Notes.notebook
February 18, 2016
Summation Notation
Examples Write each arithmetic series in summation notation.
1.) 4 + 8 + 12 + 16 + 20
2.) 100 + 90 + 80 + ... + 10
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Examples Find the sum of each finite series.
1.)
2.)
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9.4 Notes.notebook
February 18, 2016
3.) Find the sum of the series to the 20th term.
2, -2, -6, -10, ...
Homework: pages 591-593: #9-49 odd, 57-59 all
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