1 / 12

14.2, 14.4 Arithmetic and Geometric Means

14.2, 14.4 Arithmetic and Geometric Means. OBJ: • Find arithmetic and geometric means. Arithmetic means are the terms between two given terms of an arithmetic progression or sequence.

teva
Download Presentation

14.2, 14.4 Arithmetic and Geometric Means

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 14.2, 14.4 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. EX:  Find two arithmetic means between 29 and 8. 29, ____, ____, 8 l = a + (n – 1) d 8 = 29 + 3d -21 = 3d -7 = d 29, 22, 15, 8 As shown in the example below, you can find any specified number of arithmetic means between two given numbers.

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

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

  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. -8 + 22 2 14 2 7

  7. r2 = 5 r = ±5 r3 = -8 r = -2 3. r3 = _ 64 125 r = -4 5 Find the real number solution.

  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 96 . . .

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

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

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

  12. Thegeometric 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.

More Related