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Arithmetic Sequences & Series
Mr. Peter Richard, So bright that his mother calls him “sun” will teach you this series
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Arithmetic Sequence: The difference between consecutive terms is constant (or the same). The constant difference is also known as the common difference (d). (It’s also that number that you are adding everytime!)
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Example: Decide whether each sequence is arithmetic.
5,11,17,23,29,… 11-5=6 17-11=6 23-17=6 29-23=6 Arithmetic (common difference is 6) -10,-6,-2,0,2,6,10,… -6--10=4 -2--6=4 0--2=2 2-0=2 6-2=4 10-6=4 Not arithmetic (because the differences are not the same)
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ARITHMETIC SEQUENCE d= term – previous term 1. 0, -8, -16, -24,…
A sequence in which a constant d can be added to each term to get the next term. The constant d is called the common difference. d= term – previous term 1. 0, -8, -16, -24,… d = -8 d = -3 2. -3, -6, -9, -12 … d = -1/2 3. 1, 1/2, 0, -1/2 …
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Rule for an Arithmetic Sequence
an=a1+(n-1)d A(n) = nth term a = first term n = term number d = common difference
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Finding Terms of a Sequence
Find the first, fifth, and tenth terms of the sequence that has the rule A(n) = 12 + (n – 1)(-2) First term: A(1) = 12 + (1 – 1)(-2) = 12 Fifth term: A(5) = 12 + (5 – 1)(-2) = (-2) = 4 Tenth term: A(10) = 12 + (10 – 1)(-2) = (-2) = -6
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Assignment Quiz: Page 294 # 16, 22, 24, 26, 28 Homework: # 13, 23, 25, 27, 29
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