All you ever need to know about Sequences and Series

Slides:

Advertisements

Similar presentations

Chapter 8 Vocabulary. Section 8.1 Vocabulary Sequences An infinite sequence is a function whose domain is the set of positive integers. The function.

Advertisements

OBJECTIVE We will find the missing terms in an arithmetic and a geometric sequence by looking for a pattern and using the formula.

8.2 Arithmetic Sequences and Series 8.3 Geometric Sequences and Series

Sequences, Series, and the Binomial Theorem

Arithmetic Sequences and Series Unit Definition Arithmetic Sequences – A sequence in which the difference between successive terms is a constant.

Last Time Arithmetic SequenceArithmetic Series List of numbers with a common difference between consecutive terms Ex. 1, 3, 5, 7, 9 Sum of an arithmetic.

Determine whether the sequence 6, 18, 54, is geometric. If it is geometric, find the common ratio. Choose the answer from the following :

Geometric Sequences Section

Notes Over 11.3 Geometric Sequences

Warm Up Section 3.6B (1). Show that f(x) = 3x + 5 and g(x) = are inverses. (2). Find the inverse of h(x) = 8 – 3x. (3). Solve: 27 x – 1 < 9 2x + 3 (4).

Arithmetic Sequences and Series Sequences Series List with commas “Indicated sum” 3, 8, 13,

Sequences and Series (T) Students will know the form of an Arithmetic sequence.  Arithmetic Sequence: There exists a common difference (d) between each.

Sequences MATH 102 Contemporary Math S. Rook. Overview Section 6.6 in the textbook: – Arithmetic sequences – Geometric sequences.

Lesson 4-7 Arithmetic Sequences.

Warm Up Section 3.6B (1). Show that f(x) = 3x + 5 and g(x) =

Ch.9 Sequences and Series

12.2: Analyze Arithmetic Sequences and Series HW: p (4, 10, 12, 14, 24, 26, 30, 34)

Arithmetic Sequences How do I define an arithmetic sequence and how do I use the formula to find different terms of the sequence?

Ch. 11 – Sequences & Series 11.1 – Sequences as Functions.

9.2 Arithmetic Sequences. Objective To find specified terms and the common difference in an arithmetic sequence. To find the partial sum of a arithmetic.

8.6 Geometric Sequences.

Lesson #8.6: Geometric Sequence Objective: SWBAT form geometric sequences and use formulas when describing sequences.

Sequences & Series. Sequences  A sequence is a function whose domain is the set of all positive integers.  The first term of a sequences is denoted.

Review for the Test Find both an explicit formula and a recursive formula for the nth term of the arithmetic sequence 3, 9, 15,……… Explicit Formula ______________________________.

13.3 – Arithmetic and Geometric Series and Their Sums Objectives: You should be able to…

Section 12-1 Sequence and Series

Geometric Sequences and Series Section Objectives Recognize, write, and find nth terms of geometric sequences Find the nth partial sums of geometric.

Homework Questions. Geometric Sequences In a geometric sequence, the ratio between consecutive terms is constant. This ratio is called the common ratio.

Unit 5 – Series, Sequences, and Limits Section 5.2 – Recursive Definitions Calculator Required.

Arithmetic Sequences How do I define an arithmetic sequence and how do I use the formula to find different terms of the sequence?

12.2, 12.3: Analyze Arithmetic and Geometric Sequences HW: p (4, 10, 12, 18, 24, 36, 50) p (12, 16, 24, 28, 36, 42, 60)

Sum of Arithmetic Sequences. Definitions Sequence Series.

Geometric Sequences Plus a review of arithmetic sequences.

SECTION REVIEW Arithmetic and Geometric Sequences and Series.

CONSECUTIVE INTEGERS. CONSECUTIVE INTEGERS - Consecutive integers are integers that follow each other in order. They have a difference of 1 between each.

9.3 Geometric Sequences and Series. 9.3 Geometric Sequences A sequence is geometric if the ratios of consecutive terms are the same. This common ratio.

Geometric Sequence Sequences and Series. Geometric Sequence A sequence is geometric if the ratios of consecutive terms are the same. 2, 8, 32, 128, 512,...

+ 8.4 – Geometric Sequences. + Geometric Sequences A sequence is a sequence in which each term after the first is found by the previous term by a constant.

Geometric Sequences. Warm Up What do all of the following sequences have in common? 1. 2, 4, 8, 16, …… 2. 1, -3, 9, -27, … , 6, 3, 1.5, …..

13.3 Arithmetic and Geometric Series and Their Sums Finite Series.

Sequences and Series Adaped from teacherweb.com. Introduction to Sequences and Series  Sequence – 1) an ordered list of numbers. 2) a function whose.

Algebra Arithmetic Sequences and Series. Vocabulary Sequence – A list of numbers in a particular order Arithmetic Sequence – A sequence of numbers.

Review on Sequences and Series-Recursion/Sigma Algebra II.

Section 9.2 Arithmetic Sequences and Partial Sums 1.

Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the.

13.1 – Finite Sequences and Series

Chapter 13: Sequences and Series

Sequences and Series IB standard

12.1 – Arithmetic Sequences and Series

Arithmetic and Geometric Sequences

11.3 – Geometric Sequences and Series

13.3 – Arithmetic and Geometric Series and Their Sums

Arithmetic Sequences and Series

Arithmetic Sequences and Series

Section 11.1 Sequences.

Sequences and Series 4.7 & 8 Standard: MM2A3d Students will explore arithmetic sequences and various ways of computing their sums. Standard: MM2A3e Students.

Unit 5 – Series, Sequences, and Limits Section 5

Sequences and Series.

12.2 – Arithmetic Sequences and Series

Warm Up Look for a pattern and predict the next number or expression in the list , 500, 250, 125, _____ 2. 1, 2, 4, 7, 11, 16, _____ 3. 1, −3,

Plus a review of arithmetic sequences

12.2 – Arithmetic Sequences and Series

Lesson 12–3 Objectives Be able to find the terms of an ARITHMETIC sequence Be able to find the sums of arithmetic series.

Warmup Solve cos 2

Unit 5 – Series, Sequences, and Limits Section 5

Geometric Sequences and Series

12.2 – Geometric Sequences and Series

12.1 – Arithmetic Sequences and Series

Geometric Sequences and Series

Presentation transcript:

All you ever need to know about Sequences and Series

Definitions A sequence - a function whose domain is a set of consecutive integers. If the domain is not specified then it is understood that it starts with 1. An arithmetic sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference. A geometric sequence is a sequence with a common ratio, r. i.e. The ratio of successive terms in a geometric sequence is a constant called the common ratio, denoted r.

Let's play guess the sequence!: I give you a sequence and you guess the type. 3, 8, 13, 18, 23, . . . 1, 2, 4, 8, 16, . . . 24, 12, 6, 3, 3/2, 3/4, . . . 55, 51, 47, 43, 39, 35, . . . 2, 5, 10, 17, . . . 1, 4, 9, 16, 25, 36, . . .

Answers! 1) Arithmetic, the common difference d = 5 2) Geometric, the common ratio r = 2 3) Geometric, r = 1/2 4) Arithmetic, d = -4 5) Neither, why? (How about no common difference or ratio!) 6) Neither again! (This looks familiar, could it be from geometry?)

Sample problems: 1) un = 3n + 2 2) un = n2 + 1 3) un = 3(2)n Find the first four terms and state whether the sequence is arithmetic, geometric, or neither. 1) un = 3n + 2 2) un = n2 + 1 3) un = 3(2)n

Answers: 1) un = 3n + 2 To find the first four terms, in a row, replace n with 1, then 2, then 3 and 4 Answer: 5, 8, 11, 14 The sequence is arithmetic! d = 3

2) un = n2 + 1 To find the first four terms, do the same as above! Answer: 2, 5, 10, 17 The sequence is neither. Why?

3) un = 3(2)n Ditto for this one ( got it by now?) Answer: 6, 12, 24, 48 The sequence is geometric with r = 2

Arithmetic Sequences and Series

Vocabulary of Sequences (Universal)

Given an arithmetic sequence with x 38 15 NA -3 X = 80

9 x 633 NA 24 X = 27

-6 29 20 NA x

How do you find the sum of an Arithmetic Sequence?

A sequence is defined by un= 68-5n. Prove that the sequence is arithmetic. Find the first term and d. Find the 37th term Find the sum of 37 terms.

Find n for the series in which 5 y x 440 3 Graph on positive window X = 16

Arithmetic Series Practice 1. Find the sum of 3 + 7+11+15+ ….. to 20 terms 2. Find the sum of the first 10 terms of the pattern represented by 2k + 5 3. Find the sum of the first 50 multiples of 11

Each section of a soccer stadium has 44 rows with 22 seats in the first row, 23 in the second row, 24 in the third row, and so on. How many seats are there in: Row 44 Each section The stadium which has 25 sections.