sequences section 14.1. sequences suppose that a town’s present population of 100,000 is growing...
DESCRIPTION
Sequences If we continue to calculate, the town’s yearly population can be written as the infinite sequence of numbers 105,000, 110,250, 115,763, …. If we decide to stop calculating after a certain year (say, the fourth year), we obtain the finite sequence 105,000, 110,250, 115,763, 121,551TRANSCRIPT
![Page 1: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/1.jpg)
SequencesSection 14.1
![Page 2: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/2.jpg)
SequencesSuppose that a town’s present population of 100,000 is growing by 5% each year.
After the first year, the town’s population will be:100,000 + 0.05(100,000) = 105,000
After the second year, the town’s population will be:105,000 + 0.05(105,000) = 110,250
After the third year, the town’s population will be:110,250 + 0.05(110,250) ≈ 115,763
![Page 3: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/3.jpg)
SequencesIf we continue to calculate, the town’s yearly population can be written as the infinite sequence of numbers
105,000, 110,250, 115,763, ….
If we decide to stop calculating after a certain year (say, the fourth year), we obtain the finite sequence
105,000, 110,250, 115,763, 121,551
![Page 4: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/4.jpg)
Sequences An infinite sequence is a function whose
domain is the set of natural numbers {1, 2, 3, 4, …}
Ex. 2, 4, 6, 8, …
A finite sequence is a function whose domain is the set of natural numbers {1, 2, 3, 4, …, n}, where n is some natural number.
Ex. 1, -2, 3, -4, 5
![Page 5: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/5.jpg)
Writing the terms of a Sequence𝑎𝑛=2
𝑛
is known as the general term
![Page 6: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/6.jpg)
Writing the terms of a Sequence
First term Second termThird term
Tenth term
![Page 7: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/7.jpg)
Example 1:Write the first three terms of the sequence whose general term is given by .
Evaluate , where n is 1, 2, and 3.
Replace n with 1
![Page 8: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/8.jpg)
Example 1:Write the first three terms of the sequence whose general term is given by .
Evaluate , where n is 1, 2, and 3.
Replace n with 2
![Page 9: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/9.jpg)
Example 1:Write the first three terms of the sequence whose general term is given by .
Evaluate , where n is 1, 2, and 3.
Replace n with 3
![Page 10: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/10.jpg)
OYO: Write the first four terms of the sequence whose
general term is given by .
![Page 11: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/11.jpg)
Example 2:If the general term of a sequence is given by , find
a. the first term of the sequence
![Page 12: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/12.jpg)
Example 2:If the general term of a sequence is given by , find
b.
![Page 13: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/13.jpg)
Example 2:If the general term of a sequence is given by , find
c. the one-hundredth term of the sequence
![Page 14: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/14.jpg)
Example 2:If the general term of a sequence is given by , find
d.
![Page 15: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/15.jpg)
OYO: If the general term of a sequence is given by ,
finda. the first term of the sequence
b.
c. The thirtieth term of the sequence
d.
![Page 16: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/16.jpg)
Example 3: Finding the general term of a sequenceFind a general term of the sequence whose first few terms are given. a. 1, 4, 9, 16, … Terms are all squares.
![Page 17: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/17.jpg)
Example 3: Finding the general term of a sequenceFind a general term of the sequence whose first few terms are given. b. Terms are all reciprocals.
![Page 18: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/18.jpg)
Example 3: Finding the general term of a sequenceFind a general term of the sequence whose first few terms are given. c.
![Page 19: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/19.jpg)
Example 3: Finding the general term of a sequenceFind a general term of the sequence whose first few terms are given. d. Terms double each time.
![Page 20: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/20.jpg)
OYO:Find a general term of the sequence whose first few terms are given. a. b. 3, 9, 27, 81, ...
![Page 21: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/21.jpg)
Example 4: ApplicationThe amount of weight, in pounds, a puppy gains in each month of its first year is modeled by a sequence whose general term is , where n is the number of the month. Write the first five terms of the sequence, and find how much weight the puppy should gain in its fifth month.
The puppy should gain 9 pounds in its fifth month.
![Page 22: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/22.jpg)
OYO:The value v, in dollars, of an office copier depreciates according to the sequence , where n is the time in years. Find the value of the copier after three years.
The copier would only be worth $2022.40 after three years.
![Page 23: Sequences Section 14.1. Sequences Suppose that a town’s present population of 100,000 is growing by 5% each year. After the first year, the town’s population](https://reader033.vdocuments.site/reader033/viewer/2022051521/5a4d1aed7f8b9ab05997bc8b/html5/thumbnails/23.jpg)
HOMEWORK Unit 19 homework page (on the back of
your unit plan)
# 1 – 5