Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a...
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![Page 1: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/1.jpg)
Ch. 8.1:Geometric Mean
![Page 2: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/2.jpg)
pattern where the next term is found by multiplying the previous term by a factor.
Geometric Sequence
Ex: 1 , 4 , 16 , 64 , 256
What is the factor? 4
![Page 3: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/3.jpg)
Starting number: 2 Factor: 5 Create 4 terms of a geometric sequence.
Try it #1
2 , 10 , 50 , 250
![Page 4: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/4.jpg)
Find the missing term.
2 , ___ , 72 , 432
Try it #2
12
![Page 5: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/5.jpg)
Geometric Mean
The term between any terms of a geometric sequence
![Page 6: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/6.jpg)
ExampleWith a factor of 5, 20 is the geometric mean of 4 and 100.
4 , , 10020
![Page 7: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/7.jpg)
FactConsecutive terms of a geometric sequence are proportional.
a x
x b
•For any geometric sequence: a, x, b
2 6:
6 18ie ie: (2, 6, 18)
![Page 8: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/8.jpg)
Try it !
1. 10 and 40
2. 1 and 36
3. 10 and 20
4. 5 and 6
Find the geometric mean of . . .Answer = 20
Answer = 6
Answer = or 14.14
Answer = or 5.48
10 2
30
![Page 9: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/9.jpg)
How does this relate to geometry?
D CB
A
![Page 10: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/10.jpg)
Re-label the Sides (as lengths)
a bf
d ec
![Page 11: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/11.jpg)
a bf
d e
Geometric Mean #1
af
d e
fb
d
f =
f
e
f is the geometric mean of d and e.
What is the proportion that uses f?
![Page 12: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/12.jpg)
Geometric Mean #2
ba
c e
fb
a bf
d ec
e
b =
b
c
b is the geometric mean of e and c.
What is the proportion that uses b?
![Page 13: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/13.jpg)
Geometric Mean #3
d
a =
a
c
ba
c
af
d
a bf
d ec
a is the geometric mean of d and c.
What is the proportion that uses a?
![Page 14: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/14.jpg)
Put them all together
a bf
d ec
d
a =
a
c
e
b =
b
c
d
f =
f
e
a bf
d ecW
![Page 15: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/15.jpg)
Try it ! Round to hundredth
a bf
d ec
d = 4e = 10
Find:a = ___b = ___c = ___f = ___
![Page 16: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/16.jpg)
Solution:
4
f =
f
10
4
a =
a
14
10
b =
b
14
a bf
4 1014proportions
answers
142a 2 10f 2 35f
![Page 17: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/17.jpg)
Type of Triangle
1: Make sure it is a triangle
a + b > c (where c is the longest side)
2: Acute Triangle: a2 + b2 > c2
Obtuse Triangle: a2 + b2 < c2
Right Triangle: a2 + b2 = c2
![Page 18: Ch. 8.1: Geometric Mean pattern where the next term is found by multiplying the previous term by a factor. Geometric Sequence Ex: 1, 4, 16, 64, 256 What.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c36481/html5/thumbnails/18.jpg)
Name the type of triangle, if possible1) 8, 10, 12
2) 6, 12, 15
3) 13, 19, 6
4) 13, 5, 12
Answer: Acute
Answer: Obtuse
Answer: N.P.
Answer: Right