Last Time Arithmetic SequenceArithmetic Series List of numbers with a common difference between...

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Last Time Arithmetic Sequence Arithmetic Series List of numbers with a common difference between consecutive terms Ex. 1, 3, 5, 7, 9 Sum of an arithmetic sequence Ex. 1 + 3 + 5 + 7 + 9 To find the nth term in an arithmetic sequence we use To find the sum of a finite arithmetic series we use

Transcript of Last Time Arithmetic SequenceArithmetic Series List of numbers with a common difference between...

Page 1: 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.

Last TimeArithmetic Sequence Arithmetic Series

List of numbers with a common difference between consecutive terms

Ex. 1, 3, 5, 7, 9

Sum of an arithmetic sequence

Ex. 1 + 3 + 5 + 7 + 9

To find the nth term in an arithmetic sequence we use

To find the sum of a finite arithmetic series we use

Page 2: 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.

Sequence Vs. Series

Is it an arithmetic sequence or an arithmetic series?

What is the common difference (d)?

81 + 83 + 85 + 87 + ... 8, 12, 16, 20, …

4 + -3 + -10 + -17 + …

Page 3: 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.

Section 11.3Geometric Sequences and Series

Page 4: 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.

Learning goals

● Geometric Sequence● Find the nth Term● Geometric Series● Find the Sum

Page 5: 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.

Ex.

2, 4, 8, 16, … r =

r =

Geometric Sequence

Geometric Sequence has a constant (r) that when you multiply a term by r you get the next term in the sequence.We call r the common ratio

Page 6: 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.

Write out the next 3 terms in the geometric sequence

Write the first 3 terms out

a1 is our first term

Page 7: 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.

Are the following sequences geometric or arithmetic or neither?

1, 2, 4, -8, …

1, 7, 13, 19, 25, …

81, 27, 9, 3, 1, …

Page 8: 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.

81, 27, 9, 3, 1, … r =

to find a6 , a12 , an we can use the equation

Page 9: 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.

Find an of

Page 10: 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.

Geometric Series

Add the terms of a geometric sequence to get a geometric series

To find the sum of the first n terms we use:

Page 11: 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.

Find the S6 of 1 + 5 + 25 + 125 + 625 + …

Page 12: 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.

Find.

Page 13: 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.

Find n such that Sn = 341 of the geometric

series 1 + 4 + 16 + 64 + …

Page 14: 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.

SummaryGeometric Sequence Geometric Series

Sequence where you multiply a term by r to get the next term

Ex. 1, 3, 9, 27, 81

Sum of a geometric sequence

Ex. 1 + 3 + 9 + 27 + 81

To find the nth term in a geometric sequence we use

To find the sum of a finite geometric series we use


Arithmetic Sequences - Chandler Unified School District · Arithmetic Sequence In an arithmetic sequence, the difference between each pair of consecutive terms is the same. This difference

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

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

Name: Date: Period: Algebra 2 – Honors - - Summer ...€¦ · 2 more than the quotient of a number and 5 2. the sum of two consecutive integers . 3. 5 times the sum of a number

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Matrices MSU CSE 260. Outline Introduction Matrix Arithmetic: –Sum, Product Transposes and Powers of Matrices –Identity matrix, Transpose, Symmetric matrices.

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SCHEME OF STUDIES FIRST YEAR Code Subject Name T P C CIVIL CURRICULUM.pdf · 4.2 Arithmetic means. 4.3 Arithmetic series and its sum. 4.4 Geometric sequence. 4.5 Geometric means.

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up a number as a sum of Fibonacci numbers Fact: Every positive integer can be expressed uniquely as a sum of one or more distinct Fibonacci numbers no two of which are consecutive.

up a number as a sum of Fibonacci numbers Fact: Every positive integer can be expressed uniquely as a sum of one or more distinct Fibonacci numbers no two of which are consecutive.

9-1/9-2: Arithmetic Sequences and Series Objectives: Find the n th term and arithmetic means of an arithmetic sequence find the sum of n terms of an arithmetic.

9-1/9-2: Arithmetic Sequences and Series Objectives: Find the n th term and arithmetic means of an arithmetic sequence find the sum of n terms of an arithmetic.

11 x1 t14 05 sum of an arithmetic series (2013)

11 x1 t14 05 sum of an arithmetic series (2013)

Discovering the sum of an arithmetic sequence - … the sum of an arithmetic sequence Topic: ... them as tools for meaningful mathematical communication. ... (LOOKING AT INPUTS AND

Discovering the sum of an arithmetic sequence - … the sum of an arithmetic sequence Topic: ... them as tools for meaningful mathematical communication. ... (LOOKING AT INPUTS AND

FM3 - Final Exam Reviewmsubmathing.weebly.com/.../final_exam_review__fm3_.pdf · 2018. 9. 10. · 20. Find two consecutive even integers whose sum is 126. 22. Find two consecutive

FM3 - Final Exam Reviewmsubmathing.weebly.com/.../final_exam_review__fm3_.pdf · 2018. 9. 10. · 20. Find two consecutive even integers whose sum is 126. 22. Find two consecutive

Arithmetic progressions. 1.The sum, 2n(n - 2)....Arithmetic progressions. 1.The sum, Sn, ofthe first n terms of a series is given by S; =2n(n - 2). (a) Find, in terms ofn, the nth

Arithmetic progressions. 1.The sum, 2n(n - 2)....Arithmetic progressions. 1.The sum, Sn, ofthe first n terms of a series is given by S; =2n(n - 2). (a) Find, in terms ofn, the nth

 · Mathematics () (Chapter - 5) (Arithmetic Progressions) (Class 10) Exercise 5.3 10 — Question 1: Find the sum of the following APs:

 · Mathematics () (Chapter - 5) (Arithmetic Progressions) (Class 10) Exercise 5.3 10 — Question 1: Find the sum of the following APs:

Chp. 1.2 Arithmetic Series - WordPress.com · Math521B_Chp1_2_W2017_wNotes.notebook 3 February 09, 2017 Ex. 4) The Sum of the first two terms of an arithmetic sequence is 19 and the

Chp. 1.2 Arithmetic Series - WordPress.com · Math521B_Chp1_2_W2017_wNotes.notebook 3 February 09, 2017 Ex. 4) The Sum of the first two terms of an arithmetic sequence is 19 and the

Bellwork The sum of the third and fourth terms in a sequence of consecutive integers is 47. What is the sum of the first five terms of the sequence? The.

Bellwork The sum of the third and fourth terms in a sequence of consecutive integers is 47. What is the sum of the first five terms of the sequence? The.

Sequences and Series - NJCTLcontent.njctl.org/courses/math/pre-calculus/sequences... · 2015-12-04 · Arithmetic Series An arithmetic series is the sum of the terms in the arithmetic

Sequences and Series - NJCTLcontent.njctl.org/courses/math/pre-calculus/sequences... · 2015-12-04 · Arithmetic Series An arithmetic series is the sum of the terms in the arithmetic

ODD, EVEN, & CONSECUTIVE INTEGERS The sum of 2 consecutive integers is 63. Find the numbers.

ODD, EVEN, & CONSECUTIVE INTEGERS The sum of 2 consecutive integers is 63. Find the numbers.

MP Class 10 Maths Syllabus · 2020-06-08 · 8 4. ARITHMETIC PROGRESSIONS (8) Periods Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first

MP Class 10 Maths Syllabus · 2020-06-08 · 8 4. ARITHMETIC PROGRESSIONS (8) Periods Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first

Arithmetic Sequences and Series An Arithmetic Sequence is defined as a sequence in which there is a common difference between consecutive terms.

Arithmetic Sequences and Series An Arithmetic Sequence is defined as a sequence in which there is a common difference between consecutive terms.

Arithmetic Sequences and Series Sequences Series List with commas “Indicated sum” 3, 8, 13, 18 3 + 8 + 13 + 18.

Arithmetic Sequences and Series Sequences Series List with commas “Indicated sum” 3, 8, 13, 18 3 + 8 + 13 + 18.

arithmetic operation in four consecutive even and odd integers

arithmetic operation in four consecutive even and odd integers