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Chapter 1: Sequences and Series
1.1 Arithmetic Sequence
1) Derive a rule for determining the general term of an arithmetic sequence.
2) Determine t1, d, n, or tn in a problem that involves an arithmetic sequence.
3) Describe the relationship between an arithmetic sequence and a linear function.
4) Solve problems involving arithmetic sequences.
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In 1705, Edmond Halley predicted that the comet seen in 1531, 1607, and 1682 would be seen again in 1758. Halley's prediction was accurate. This comet is now renown as Halley's Comet. The years in which Halley's Comet appears forms terms of an arithmetic sequence. What makes this sequence arithmetic?
When can earthlings next expect to see Halley's Comet?
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Sequence an ordered list of objects that adhere to a pattern.
Finite Sequence finite number of terms (know when it ends)
Infinite Sequence infinite number of terms (does not end).
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Arithmetic Sequence a sequence in which the difference between consecutive terms is constant (common term added/subtracted to the previous term)
Geometric Sequence a sequence in which the ratio of consecutive terms is constant (common ratio multiplying or dividing by same value)
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1) 3,6,12,24,...
2) 1,2,4,7,11,16,...
3) 4,12,6,18,9,...
4) 1,4,9,16,25,...
5) A,D,G,J,
6) 1,Z,4,Y,8,X,13,...
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Deriving the formula:t1 = t1t2 = t1 + d
20,25,30,35,... t1,t2,t3,t4,...
d = common difference
d = d =
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t1 the first term in a sequence (some texts will call it "a")
n the number of terms in a sequence
tn the nth term or the general term
d the common difference (specific to arithmetic sequences)
tn = t1 + (n 1)d
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Many factors affect the growth of a child. Medical and health officials encourage parents to keep track of their child’s growth. The general guideline for the growth in height of a child between the ages of 3 years and 10 years is an average increase of 5 cm per year. Suppose a child was 70 cm tall at age 3.a) Write the general term that you could use to estimate what the child’s height will be at any age between 3 and 10.b) How tall is the child expected to be at age 10?
e.g. (1)
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e.g. (2)
Suppose that the growth of the colony of ants produces an arithmetic sequence in which the number of ants increases by approximately 80 ants each month. Beginning with 40 ants, how many months would it take for the ant population to reach 3000?
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e.g. (3)
Jonathon has a parttime job at the local grocery store. He has been asked to create a display of cereal boxes. The top six rows of his display are shown. The numbers of boxes in the rows produce an arithmetic sequence. There are 16 boxes in the third row from the bottom, and 6 boxes in the eighth row from the bottom.a) How many boxes are in the bottom row?b) Determine the general term, tn, for the sequence.c) What is the number of rows of boxes in his display?
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e.g. (4)A furnace technician charges $65 for making a house call, plus $42 per hour or portion of an hour.
a) Generate the possible charges for the first four
hours of time.
b) What is the charge for 10 h of time?
c) Is this function continuous or discrete? Explain.
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Check Your Understanding:
pages 1619
#17, 9, 13, 15, 17, 21