Sullivan Algebra and Trigonometry: Section 13.2 Objectives of this Section Determine If a Sequence Is Arithmetic Find a Formula for an Arithmetic Sequence.

Slides:

Advertisements

Similar presentations

Choi 2012 Arithmetic Sequence A sequence like 2, 5, 8, 11,…, where the difference between consecutive terms is a constant, is called an arithmetic sequence.

Advertisements

Warm Up Find the nth term of the sequence 3, 6, 9, 12, … (Hint: what is the pattern?) Find the 11 th term.

Arithmetic Sequences Finding the nth Term. Arithmetic Sequences A pattern where all numbers are related by the same common difference. The common difference.

4.7 Arithmetic Sequences A sequence is a set of numbers in a specific order. The numbers in the sequence are called terms. If the difference between successive.

1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 10 Further Topics in Algebra.

Arithmetic Sequences & Partial Sums Pre-Calculus Lesson 9.2.

Arithmetic Sequences Section 4.5. Preparation for Algebra ll 22.0 Students find the general term and the sums of arithmetic series and of both finite.

SECTION 7.2 ARITHMETIC SEQUENCES. (a) 5, 9, 13, 17, 21,25 (b) 2, 2.5, 3, 3.5, 4, 4, (c) 8, 5, 2, - 1, - 4, - 7 Adding 4 Adding.5 Adding - 3 Arithmetic.

Arithmetic Sequences (Recursive Formulas). Vocabulary sequence – a set of numbers in a specific order. terms – the numbers in the sequence. arithmetic.

Section 9.2 Arithmetic Sequences. OBJECTIVE 1 Arithmetic Sequence.

1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 11 Further Topics in Algebra.

Section 7.2 Arithmetic Sequences Arithmetic Sequence Finding the nth term of an Arithmetic Sequence.

Section 11.2 Arithmetic Sequences IBTWW:

12-1 Arithmetic Sequences and Series. Sequence- A function whose domain is a set of natural numbers Arithmetic sequences: a sequences in which the terms.

2, 4, 6, 8, … a1, a2, a3, a4, … Arithmetic Sequences

Arithmetic Sequences and Series

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

ARITHMETIC SEQUENCES. (a) 5, 9, 13, 17, 21,25 (b) 2, 2.5, 3, 3.5, 4, 4, (c) 8, 5, 2, - 1, - 4, - 7 Adding 4 Adding.5 Adding - 3 Arithmetic Sequences.

Warm Up State the pattern for each step.

Notes Over 11.2 Arithmetic Sequences An arithmetic sequence has a common difference between consecutive terms. The sum of the first n terms of an arithmetic.

12.2 & 12.5 – Arithmetic Sequences Arithmetic : Pattern is ADD or SUBTRACT same number each time. d = common difference – If add: d positive – If subtract:

Section 12-1 Sequence and Series

Review of Sequences and Series.  Find the explicit and recursive formulas for the sequence:  -4, 1, 6, 11, 16, ….

13.4 Geometric Sequences and Series Example:3, 6, 12, 24, … This sequence is geometric. r is the common ratio r = 2.

Arithmetic Sequences In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To.

Aim: What is the arithmetic series ? Do Now: Find the sum of each of the following sequences: a) b)

Essential Questions Series and Summation Notation

Arithmetic Sequences Sequence is a list of numbers typically with a pattern. 2, 4, 6, 8, … The first term in a sequence is denoted as a 1, the second term.

Review of Sequences and Series

Arithmetic Sequences. Arithmetic sequence Before talking about arithmetic sequence, in math, a sequence is a set of numbers that follow a pattern. We.

Arithmetic Sequences Recognize and extend arithmetic sequences.

Arithmetic Recursive and Explicit formulas I can write explicit and recursive formulas given a sequence. Day 2.

Unit 9: Sequences and Series. Sequences A sequence is a list of #s in a particular order If the sequence of numbers does not end, then it is called an.

Unit 4: Sequences & Series 1Integrated Math 3Shire-Swift.

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.

Arithmetic Sequences & Partial Sums

Section 4-7: Arithmetic Sequences.

Recognize and extend arithmetic sequences

4-7 Arithmetic Sequences

11.2 Arithmetic Sequences.

Warm Up Complete the table… Recursive Formula Sequence

The sum of the first n terms of an arithmetic series is:

Arithmetic Sequences Explicit Formulas.

11.3 Geometric sequences; Geometric Series

Sequences and Series.

Patterns & Sequences Algebra I, 9/13/17.

7-8 Notes for Algebra 1 Recursive Formulas.

Chapter 12 – Sequences and Series

WARM UP State the pattern for each set.

Sequences & Series.

Unit 1 Test #3 Study Guide.

Coordinate Algebra Day 54

4-7 Sequences and Functions

Notes Over 11.5 Recursive Rules

Section 2.1 Arithmetic Sequences and Series

Arithmetic Sequences In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To.

Arithmetic Sequence A sequence of terms that have a common difference between them.

Section 12.1 Sequences and Section 12.2 Arithmetic Sequences

Sullivan Algebra and Trigonometry: Section 13.1

The nth term, Un Example If we are given a formula for Un (th nth term) where find the first five terms of the sequence Un = 3n + 1.

Module 3 Arithmetic and Geometric Sequences

Write the recursive and explicit formula for the following sequence

Arithmetic Sequence A sequence of terms that have a common difference between them.

Arithmetic Sequence A sequence of terms that have a common difference (d) between them.

Section 9.3 Arithmetic Sequences

Module 3 Arithmetic and Geometric Sequences

Finding the nth term Example

4-7 Arithmetic Sequences

Warm Up Write the first 4 terms of each sequence:

Presentation transcript:

Sullivan Algebra and Trigonometry: Section 13.2 Objectives of this Section Determine If a Sequence Is Arithmetic Find a Formula for an Arithmetic Sequence Find the Sum of an Arithmetic Sequence

An arithmetic sequence is defined as d is called the common difference between terms of the sequence. The terms of an arithmetic sequence with the first term a and common difference d follow the pattern: a, a + d, a + 2d, a + 3d, …..

Common difference does not depend on n, therefore the sequence is arithmetic.

The nth Term of an Arithmetic Sequence

The 6th term of an arithmetic sequence is 31. The 19th term is 109. Find the first term and the common difference. Give a recursive formula for the sequence.

So, the nth term is: To find the n+1 term in terms of the nth term:

Sum of n Terms of an Arithmetic Sequence

Find the sum of the first 30 terms of the sequence {7n + 2}. That is, find