Arithmetic Sequences & Partial Sums Pre-Calculus Lesson 9.2.

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

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.
8.2 Arithmetic Sequences and Series 8.3 Geometric Sequences and Series
9.2 Arithmetic Sequences and Partial Sums
Arithmetic Sequences and Series days Digital Lesson.
Essential Question: What is a sequence and how do I find its terms and sums? How do I find the sum & terms of geometric sequences and series?
Arithmetic Sequences and Series Unit Definition Arithmetic Sequences – A sequence in which the difference between successive terms is a constant.
1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 10 Further Topics in Algebra.
Geometric Sequences and Series
Geometric Sequences and Series A sequence is geometric if the ratios of consecutive terms are the same. 2, 8, 32, 128, 512,... Definition of Geometric.
Arithmetic Sequences and Series
Arithmetic Sequences and Partial Sums
Understanding 8.1… Use sigma notation to write the sum of.
Arithmetic Sequences & Series Pre-Calculus Section.
ARITHMETIC SEQUENCES AND SERIES
Honors Precalculus: Do Now Find the nth term of the sequence whose first several terms are given. Find the first 4 terms of the given recursively defined.
9.2 Arithmetic Sequence and Partial Sum Common Difference Finite Sum.
ARITHMETIC SEQUENCES. 7, 11, 15, 19, …… Because this sequence has a common difference between consecutive terms of 4 it is an arithmetic sequences.
12.2 – Analyze Arithmetic Sequences and Series. Arithmetic Sequence: The difference of consecutive terms is constant Common Difference: d, the difference.
Wednesday, March 7 How can we use arithmetic sequences and series?
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
SFM Productions Presents: Another fun day of Pre-Calculus excitement! 9.2Arithmetic Sequences and Partial Sums.
Section 7.2 Arithmetic Sequences Arithmetic Sequence Finding the nth term of an Arithmetic Sequence.
Pre-Calculus Section 8.2B Arithmetic Sequences
Sullivan Algebra and Trigonometry: Section 13.2 Objectives of this Section Determine If a Sequence Is Arithmetic Find a Formula for an Arithmetic Sequence.
Section 11.2 Arithmetic Sequences IBTWW:
{ 12.2 Arithmetic Sequences and Series SWBAT recognize an arithmetic sequence SWBAT find the general nth term of an arithmetic sequence SWBAT evaluate.
Arithmetic Sequences and Series
THE BEST CLASS EVER…ERRR…. PRE-CALCULUS Chapter 13 Final Exam Review.
Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Copyright © Cengage Learning. All rights reserved. 8.2 Arithmetic Sequences and Partial Sums.
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.
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.
13.3 – Arithmetic and Geometric Series and Their Sums Objectives: You should be able to…
Arithmetic Sequences In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To.
Geometric Sequences & Series
Lesson 10.1, page 926 Sequences and Summation Notation Objective: To find terms of sequences given the nth term and find and evaluate a series.
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.
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.
Honors Precalculus Day 3 Section 11.3 Geometric Sequences The end of new material…BOO!!! 3/12/2016.
Algebra Arithmetic Sequences and Series. Vocabulary Sequence – A list of numbers in a particular order Arithmetic Sequence – A sequence of numbers.
Arithmetic Sequences and Series Section Objectives Use sequence notation to find terms of any sequence Use summation notation to write sums Use.
Section 8.2 Arithmetic Sequences & Partial Sums. Arithmetic Sequences & Partial Sums A sequence in which a set number is added to each previous term is.
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.
Arithmetic Sequences & Partial Sums
Arithmetic Sequences and Series
©2001 by R. Villar All Rights Reserved
Geometric Sequences and Series
11.2 Arithmetic Sequences.
The sum of the first n terms of an arithmetic series is:
13.3 – Arithmetic and Geometric Series and Their Sums
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Arithmetic Sequences & Series
Arithmetic Sequences and Series
Warm-up Problems Consider the arithmetic sequence whose first two terms are 3 and 7. Find an expression for an. Find the value of a57. Find the sum of.
Aim: What is the geometric series ?
Chapter 12 – Sequences and Series
WARM UP State the pattern for each set.
4-7 Sequences and Functions
ex. 2, 7, 12, 17, 22, 27 5 is the common difference. an+1 = an + d
Sequences and Series.
Geometric Sequences and Series
Geometric Sequences.
Arithmetic Sequences In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To.
Geometric Sequences and Series
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Geometric Sequence Skill 38.
Recognizing and extending arithmetic sequences
8-2 Analyzing Arithmetic Sequences and Series
Presentation transcript:

Arithmetic Sequences & Partial Sums Pre-Calculus Lesson 9.2

An Arithmetic Sequence is a sequence whose consecutive terms have a common difference, d.

5. Find the first three terms of the arithmetic sequence with a 1 = 300 and d = Find the first three terms of the arithmetic sequence with a 1 = 220 and d = -25.

a n = a 1 + (n – 1)d To find the nth term of an arithmetic sequence with first term a 1 and common difference d, use the following formula

7. Write a formula for the general term of the arithmetic sequence 2, 7, 12, 17…

8. Find the eighth term of the arithmetic sequence whose first term is 4 and whose common difference is – Find the ninth term of the arithmetic sequence that begins with 2 and Find a 6 when a 1 = 13 and d = 4.

Sum of a Finite Arithmetic Sequence, called S n :

11.Find the sum: Find the sum of the integers from 1 to 100.

13.Find the 150 th partial sum of the arithmetic sequence: 5, 16, 27, 38, 49…

14. Find the following sum: