finite sequence finite number of terms (know when it ends)
TRANSCRIPT
Day 1 Arithmetic Sequence.notebook
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November 29, 2017
Sep 29:50 AM
Sequences and Series
Sequence An ordered list of objects that adhere to a pattern.
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 by same value)
Finite Sequence Finite number of terms (know when it ends)
Infinite Sequence Infinite number of terms (does not end)
Day 1 Arithmetic Sequence.notebook
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November 29, 2017
May 259:26 AM
Arithmetic Sequence
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
tn = t1 + (n 1)d
General Term: a question specific equation you create using the formula
Day 1 Arithmetic Sequence.notebook
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November 29, 2017
May 259:30 AM
Ex(1) Write the general term for the following sequences and find t22
a) 6,13, 20, 27,...
b) 9, 4, 1,...
tn = t1 + (n 1)d
Day 1 Arithmetic Sequence.notebook
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November 29, 2017
Sep 210:17 AM
Ex(2) A visual and performing arts group wants to hire a community events leader. The person will be paid $12 for the first hour of work, $19 for two hours of work, $26 for three hours of work, and so on.
a) Write the general term that you could use to determine the pay for any number of hours worked.
b) What will the person get paid for 6 h of work?
Day 1 Arithmetic Sequence.notebook
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November 29, 2017
May 259:45 AM
You Try: 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?
Day 1 Arithmetic Sequence.notebook
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November 29, 2017
May 259:49 AM
Ex(3) The muskox and the caribou of northern Canada are hoofed mammals that survived the Pleistocene Era, which ended 10 000 years ago. In 1955, the Banks Island muskox population was approximately 9250 animals. Suppose that in subsequent years, the growth of the muskox population generated an arithmetic sequence, in which the number of muskox increased by approximately 1650 each year.
How many years would it take for the muskox population to reach 100 000?
Day 1 Arithmetic Sequence.notebook
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November 29, 2017
May 252:28 PM
You Try: 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?
Day 1 Arithmetic Sequence.notebook
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November 29, 2017
May 252:30 PM
Ex(4) 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?
See page 13 of the textbook for how to do this question using algebra!
Day 1 Arithmetic Sequence.notebook
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November 29, 2017
May 258:38 PM
You Try: Jonathon has been given the job of stacking cans in a similar design to that of the cereal boxes. The numbers of cans in the rows produces an arithmetic sequence. The top three rows are shown. There are 14 cans in the 8th row from the bottom and 10 cans in the 12th row from the bottom. Determine t1, d, and tn for the arithmetic sequence.
Day 1 Arithmetic Sequence.notebook
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November 29, 2017
Sep 211:00 AM
Practice:
p. 1619, #1, 2ab, 3, 4ac, 5acd, 6, 7, 9, 13, 14, 15, 16, 19, 22, 23