Download presentation

1
**Arithmetic and Geometric Means**

OBJ: • Find arithmetic and geometric means

2
**Arithmetic means are the terms between two given terms of an arithmetic progression or sequence.**

For example, three arithmetic means between 2 and 18 in the progression below are 6, 10, and 14 since 2, 6, 10, 14, 18, is an arithmetic progression. 2, 6, 10, 14, 18, . . .

3
As shown in the example below, you can find any specified number of arithmetic means between two given numbers. EX: Find two arithmetic means between 29 and 8. 29, ____, ____, 8 an = a1 + (n – 1) d 8 = d -21 = 3d -7 = d 29, 22, 15, 8

4
As shown in the example below, you can find any specified number of arithmetic means between two given numbers. EX: Find the five arithmetic means between 30 and 21. 30,__,__,__,__,__, 21 an = a1 + (n – 1) d 21 = d -9 = 6d -1.5 = d 30, 28.5, 27, 25.5, 24, 22.5,21

5
As shown in the example below, you can find any specified number of arithmetic means between two given numbers. EX: Find the one arithmetic mean between 5 and 17. 5, ____, 17 an = a1 + (n – 1) d 17 = 5 + 2d 12 = 2d 6 = d 5, 11, 17

6
Since this is the same as the average of 5 and 17, it easier to use the formula: x + y. 2 which is called the arithmetic mean of the real numbers x and y. EX: Find the arithmetic mean of -8 and 22. 2 14 7

7
**Find the real number solution.**

125 r = -4 5

8
**Geometric means are the terms between two given terms of a geometric progression or sequence.**

For example, four geometric means between 3 and 96 in the progression below are 6, 12, 24, and 48 since 3, 6, 12, 24, 48, 96, is a geometric progression. 3, 6, 12, 24, 48, and

9
As shown in the example below, you can find any specified number of geometric means between two given numbers. EX: Find the two real geometric means between –3 and -3, ____, ____, 24 8 l = a •rn – 1 24 = -3 •r 3 -64 = r 3 -4 = r

10
As shown in the example below, you can find any specified number of geometric means between two given numbers. EX: Find three geometric means between 32 and 2. 32, ____, ____, ____, 2 l = a •rn – 1 2 = 32 •r4 1 = r4 16 ± 1 2

11
As shown in the example below, you can find any specified number of geometric means between two given numbers. EX: Find one geometric mean between 5 and 10 5, ____, 10 l = a •rn – 1 10 = 5 •r2 2 = r2 ±2

12
**The geometric mean (mean proportional) of the real numbers x and y (xy > 0) is**

xy or – xy . EX: Find the positive geometric mean of 4 and 8.

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google