Transcript Angles, Degrees, and Special Triangles

Arithmetic Sequences & Partial
Sums
MATH 109 - Precalculus
S. Rook
Overview
• Section 9.2 in the textbook:
– Arithmetic sequences
– Partial sums of arithmetic sequences
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Arithmetic Sequences
Arithmetic Sequences
• Arithmetic sequence: a sequence where the
difference between ANY two successive terms
is equal to the same constant value
– i.e. ai+1 – ai = d for every natural number i where d
is the difference
• e.g.  1, 2 ,5 ,8 ,  ,3 n  4 starts at -1 with a difference of 3
• e.g. 2 , 5 ,3, 7 ,  , n  3 starts at 2 with a difference of ½
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2
2
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Arithmetic Sequences (Continued)
• The formula for the nth term of an arithmetic
sequence is a  a  n  1d where a1 is the first
term of the sequence and d is the difference
between any two successive terms
n
1
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Arithmetic Sequences (Example)
Ex 1: Find the indicated term of the arithmetic
sequence:
a) Find the 12th term of the arithmetic sequence where
the first term is -1 and the second term is 3
b) Find the 20th term of the arithmetic sequence where
the first term is 2 and the fifth term is 4
c) Find the 50th term of the arithmetic sequence where
the seventh term is -27 and the eighth term is -30
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Partial Sums of Arithmetic
Sequences
Partial Sums of Arithmetic
Sequences
• The nth partial sum of an arithmetic sequence
n
 a  a  where a is the first term
S

is given by
1
2
and an is the nth term
n
1
n
– Also known as an Arithmetic Series
• Do not worry about deriving the formula –
just know how to use it
• VERY important to know the difference
between sequences and series:
– A sequence is a LIST of TERMS
– A series is a SUM of the terms of a sequence
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Partial Sums of Arithmetic
Sequences (Example)
Ex 2: Find the indicated partial sum of the
arithmetic sequence:
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a)  7 i  6
i 1
b) n = 16; first three terms are ½ , -¼ , -1
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Partial Sums of Arithmetic
Sequences – Application (Example)
Ex 3: A bookseller has an offer where the first copy of
a particular textbook is sold at full price which is
$100. Subsequent copies of the same textbook
bought in the same order will be discounted $3.00
with a limit of ten textbooks per order. (i.e. first
costs $100, second costs $97, third costs $94, etc)
a) Write an arithmetic sequence an that represents
the price of the nth textbook purchased in the same
order
b) Excluding taxes, find how much a customer will
pay for purchasing 9 textbooks on the same order
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Summary
• After studying these slides, you should be able to:
– Derive the formula for the nth term of an arithmetic
sequence given at least two terms
– Calculate the nth partial sum of an arithmetic sequence
– State the difference between sequences and series
• Additional Practice
– See the list of suggested problems for 9.2
• Next lesson
– Geometric Sequences & Series (Section 9.3)
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