Download presentation

Presentation is loading. Please wait.

1
**12.1 – Arithmetic Sequences and Series**

2
An introduction………… Arithmetic Series Sum of Terms Geometric Series Sum of Terms Arithmetic Sequences Geometric Sequences ADD To get next term MULTIPLY To get next term

3
**Find the next four terms of –9, -2, 5, …**

Arithmetic Sequence 7 is referred to as the common difference (d) Common Difference (d) – what we ADD to get next term Next four terms……12, 19, 26, 33

4
**Find the next four terms of 0, 7, 14, …**

Arithmetic Sequence, d = 7 21, 28, 35, 42 Find the next four terms of x, 2x, 3x, … Arithmetic Sequence, d = x 4x, 5x, 6x, 7x Find the next four terms of 5k, -k, -7k, … Arithmetic Sequence, d = -6k -13k, -19k, -25k, -32k

5
**Vocabulary of Sequences (Universal)**

6
**Given an arithmetic sequence with**

x 38 15 NA -3 X = 80

7
-19 353 ?? 63 x 6

8
Try this one: 1.5 16 x NA 0.5

9
9 x 633 NA 24 X = 27

10
-6 29 20 NA x

11
**Find two arithmetic means between –4 and 5**

-4, ____, ____, 5 -4 5 4 NA x The two arithmetic means are –1 and 2, since –4, -1, 2, 5 forms an arithmetic sequence

12
**Find three arithmetic means between 1 and 4**

1, ____, ____, ____, 4 1 4 5 NA x The three arithmetic means are 7/4, 10/4, and 13/4 since 1, 7/4, 10/4, 13/4, 4 forms an arithmetic sequence

13
**Find n for the series in which**

5 y x 440 3 Graph on positive window X = 16

14
**12.2 – Geometric Sequences and Series**

15
Arithmetic Series Sum of Terms Geometric Series Sum of Terms Arithmetic Sequences Geometric Sequences ADD To get next term MULTIPLY To get next term

16
**Vocabulary of Sequences (Universal)**

17
**Find the next three terms of 2, 3, 9/2, ___, ___, ___**

3 – 2 vs. 9/2 – 3… not arithmetic

18
1/2 x 9 NA 2/3

19
**Find two geometric means between –2 and 54**

-2, ____, ____, 54 -2 54 4 NA x The two geometric means are 6 and -18, since –2, 6, -18, 54 forms an geometric sequence

20
-3, ____, ____, ____

21
x 9 NA

22
x 5 NA

23
***** Insert one geometric mean between ¼ and 4*****

*** denotes trick question 1/4 3 NA

24
1/2 7 x

25
**Section 12.3 – Infinite Series**

26
1, 4, 7, 10, 13, …. Infinite Arithmetic No Sum 3, 7, 11, …, 51 Finite Arithmetic 1, 2, 4, …, 64 Finite Geometric 1, 2, 4, 8, … Infinite Geometric r > 1 r < -1 No Sum Infinite Geometric -1 < r < 1

27
**Find the sum, if possible:**

28
**Find the sum, if possible:**

29
**Find the sum, if possible:**

30
**Find the sum, if possible:**

31
**Find the sum, if possible:**

32
**The Bouncing Ball Problem – Version A**

A ball is dropped from a height of 50 feet. It rebounds 4/5 of it’s height, and continues this pattern until it stops. How far does the ball travel? 50 40 40 32 32 32/5 32/5

33
**The Bouncing Ball Problem – Version B**

A ball is thrown 100 feet into the air. It rebounds 3/4 of it’s height, and continues this pattern until it stops. How far does the ball travel? 100 100 75 75 225/4 225/4

34
Sigma Notation

35
UPPER BOUND (NUMBER) SIGMA (SUM OF TERMS) NTH TERM (SEQUENCE) LOWER BOUND (NUMBER)

39
**Rewrite using sigma notation: 3 + 6 + 9 + 12**

Arithmetic, d= 3

40
**Rewrite using sigma notation: 16 + 8 + 4 + 2 + 1**

Geometric, r = ½

41
**Rewrite using sigma notation: 19 + 18 + 16 + 12 + 4**

Not Arithmetic, Not Geometric

42
**Rewrite the following using sigma notation:**

Numerator is geometric, r = 3 Denominator is arithmetic d= 5 NUMERATOR: DENOMINATOR: SIGMA NOTATION:

Similar presentations

OK

Basel-ICU-Journal Challenge18/20/2014. 2Basel-ICU-Journal Challenge8/20/2014.

Basel-ICU-Journal Challenge18/20/2014. 2Basel-ICU-Journal Challenge8/20/2014.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on neural networks Ppt on forward rate agreement ppt Types of window display ppt online Ppt on amplitude shift keying experiment Ppt on hdfc bank Ppt on design of earthen dam Ppt on media literacy Ppt on microcontroller based temperature sensor Ppt on different solid figures first grade Ppt on mid day meal