# Introduction to Arithmetic Sequences and Series

Learn about arithmetic sequences where the next term is obtained by adding a constant difference, and arithmetic series where the sum of each term is calculated. Also compare with geometric sequences where the next term is obtained by a constant multiplier.

## About Introduction to Arithmetic Sequences and Series

PowerPoint presentation about 'Introduction to Arithmetic Sequences and Series'. This presentation describes the topic on Learn about arithmetic sequences where the next term is obtained by adding a constant difference, and arithmetic series where the sum of each term is calculated. Also compare with geometric sequences where the next term is obtained by a constant multiplier.. The key topics included in this slideshow are . Download this presentation absolutely free.

## Presentation Transcript

Slide2An introduction…………Arithmetic Sequences ADD To get next term Geometric Sequences MULTIPLY To get next term Arithmetic Series Sum of Terms Geometric Series Sum of Terms

Slide3Find 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

Slide4Find 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

Slide6Given an arithmetic sequence withx 15 38 NA -3 X = 80

Slide7-1963 ?? x 6 353

Slide8Try this one:1.5 16 x NA 0.5

Slide99x 633 NA 24 X = 27

Slide10-629   20 NA x

Slide11Find two arithmetic means between –4 and 5-4, ____, ____, 5 -4 4 5 NA x The two arithmetic means are –1 and 2, since –4,  -1, 2 , 5 forms an arithmetic sequence

Slide12Find three arithmetic means between 1 and 41, ____, ____, ____, 4 1 5 4 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

Slide13Find n for the series in which5 x y 440 3 X = 16 Graph on positive window

Slide15Arithmetic SequencesADD To get next term Geometric Sequences MULTIPLY To get next term Arithmetic Series Sum of Terms Geometric Series Sum of Terms

Slide17find the next three terms of 2, 3, 9/2, ___, ___, ___3 – 2 vs. 9/2 – 3… not arithmetic

Slide181/2x 9 NA 2/3

Slide19Find 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

Slide20-3, ____, ____, ____

Slide21x9 NA

Slide22x5 NA

Slide23*** Insert one geometric mean between ¼ and 4****** denotes trick question 1/4 3 NA

Slide241/27 x

Slide261, 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

Slide27Find the sum, if possible:

Slide28Find the sum, if possible:

Slide29Find the sum, if possible:

Slide30Find the sum, if possible:

Slide31Find the sum, if possible:

Slide32The Bouncing Ball Problem – Version AA 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 32 32/5 40 32 32/5

Slide33The Bouncing Ball Problem – Version BA 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 75 225/4 100 75 225/4

Slide34Sigma Notation

Slide35UPPER BOUND(NUMBER) LOWER BOUND (NUMBER) SIGMA (SUM OF TERMS) NTH TERM (SEQUENCE)

Slide39Rewrite using sigma notation:  3 + 6 + 9 + 12Arithmetic, d= 3

Slide40Rewrite using sigma notation:  16 + 8 + 4 + 2 + 1Geometric, r = ½

Slide41rewrite using sigma notation:  19 + 18 + 16 + 12 + 4Not Arithmetic, Not Geometric 19 + 18 + 16 + 12 + 4     -1      -2     -4    -8

Slide42Rewrite the following using sigma notation:Numerator is geometric, r = 3 Denominator is arithmetic d= 5 NUMERATOR: DENOMINATOR: SIGMA NOTATION: