Arithmetic Sequences - Cisd
Algebra I Unit 10: Arithmetic & Geometric Sequences Arithmetic Sequences Objectives Students will be able to identify if a sequence is arithmetic. Students will be able to determine the value of a specific term. Students will be able to write arithmetic sequences in explicit form. Students will be able to write arithmetic sequences in recursive form. In this course we will deal with two kinds of sequences, and . A sequence is just a list of . Each number in that sequence represents a in the sequence. Where the number is in the sequence indicates what term it is. For sequences, we use the variable to represent the term. If you were looking for the 12th term, the value of n would be . Example: {3, 13, 23, 33, 43, } What number is in the first term? Create a table using the terms in the sequence. 3rd term 5th term 15th term Term Sequence Value Are the values in the table the only values of the sequence? An sequence occurs when the same number is added to each term in the sequence. Look at the sequence in the example. Does it represent an arithmetic sequence? , because . In sequences, the number that is added to each term to find the next term is called the . We often use the variable to represent the common difference. What is the common difference of the sequence in the example? Math Department TEKS: A.12D 2015 - 2016
Algebra I Unit 10: Arithmetic & Geometric Sequences For each of the following sequences, determine if they are arithmetic or not. If they are an arithmetic sequence, determine the common difference. If they are not an arithmetic sequence, state why they do not classify. Sequence {35, 32, 29, 26, } Arithmetic? Common Difference 1st Term 7th Term { 3, 23, 43, 63, } {1, 2, 4, 8, 16, } { 7, 9, 11, 13, } {9, 14, 19, 24, } Arithmetic Sequence Formulas An equation that can be used to find the ππ‘β term of the sequence is called the . An equation that can used to find a term if the previous term is known is called . Explicit Formula ππ ππ (π π)π Where ππ Recursive Formula π ππ 1 π π *Can be used to find any term. *Can be used to find a term if the previous term is known. ππ ππ 1 π Where ππ Letβs practice writing these formulas: Sequence Explicit form Recursive form {1, 5, 9, 13, 17, } {9, 7, 5, 3, 1, } {15, 30, 45, 60, 75, } *Most explicit forms you will deal with will be simplified and will look like format. Practice getting the first explicit form in the table in π¦ ππ₯ π format. Math Department TEKS: A.12D 2015 - 2016
Algebra I Unit 10: Arithmetic & Geometric Sequences Writing Explicit Form equations When given a sequence of numbers 1. Rewrite the sequence in table form. 2. Type the table into a list & spreadsheet 3. Add a data & statistics page 4. Calculate a linear line of regression 5. Your calculator will give you x, but you know that will be Example: Write an equation in explicit form that can be used to find the ππ‘β term of the given sequence. {5, 3, 1, 1, 3, } When given a term & common difference By now we know that the common difference in explicit form is in the same place as the in mx b format. We can also say that the value of the term represents a value and the term itself represents the value. So when given term and the common difference: 1. 2. 3. 4. 5. Write the term as a coordinate. Plug in the coordinate for x & y. Plug the common difference in for . Solve for . Once you know what and are, you can write it in explicit form. Math Department TEKS: A.12D 2015 - 2016
Algebra I Unit 10: Arithmetic & Geometric Sequences Practice: Given the term and common difference below, write a function in explicit form that represents the ππ‘β term of the sequence. π1 35, π 4 Explicit form ππ ππ 11 7π π14 11 1 π 8 2 π27 ππ ππ 7.1 2.1π Term Value of the term π106 176 ππ 4 5π For each arithmetic sequence below, determine the explicit form that would find the ππ‘β value of the term. { 30, 40, 50, 60, } π1 38, π 100 {9, 14, 19, 24, } π37 249, π 8 Math Department TEKS: A.12D 2015 - 2016
Algebra I Unit 10: Arithmetic & Geometric Sequences Letβs practice using recursive form: Recursive form In words π1 ππ ππ 1 5 3 ππ 4ππ 1 1 0 1 ππ ππ 1 2 2 6 ππ 6ππ 1 4 -2 ππ 1 1 3 9 ππ Math Department TEKS: A.12D 1st 5 terms of the sequence 2015 - 2016
Algebra I Unit 10: Arithmetic & Geometric Sequences Math Department TEKS: A.12D 2015 - 2016 Arithmetic Sequences Objectives Students will be able to identify if a sequence is arithmetic. Students will be able to determine the value of a specific term. Students will be able to write arithmetic sequences in explicit form.
3.2 Arithmetic series: the sum of an arithmetic sequence Analysis, interpretation and prediction where a model is not perfectly arithmetic in real life. 7C 7D Arithmetic Sequence Arithmetic Series 6C 6D Arithmetic sequences Arithmetic series 3.1 3.2 Arithmetic sequence Arithmetic s
arithmetic sequence are called arithmetic means. In the sequence below, 38 and 49 are the arithmetic means between 27 and 60. 5, 16, 27, 38 , 49 , 60 760 Chapter 12 Sequences and Series The n th term of an arithmetic sequence with first term a 1 and common difference d is given by a n a 1 (n 1) d . The n th Term of an Arithmetic Sequence .
Arithmetic & Geometric Sequences Worksheet Level 2: Goals: Identify Arithmetic and Geometric Sequences Find the next term in an arithmetic sequence Find the next term in a geometric sequence Practice #1 Does this pattern represent an arithmetic or geometric sequence? Explain. Find how many dots would be in the next figure?
Arithmetic & Geometric Sequences Worksheet Level 2: Goals: Identify Arithmetic and Geometric Sequences Find the next term in an arithmetic sequence Find the next term in a geometric sequence Practice #1 Does this pattern represent an arithmetic or geometric sequence? Explain. Find how many dots would be in the next figure?
arithmetic sequence finds the nth term of an arithmetic sequence lists down the first few terms of an arithmetic sequence given the general term and vice-versa solves word problems involving arithmetic mean applies the concepts of mean and the nth term of an arithmetic sequence
Arithmetic Series: A series whose terms form an arithmetic sequence. 11 4 Arithmetic Series 7 April 27, 2009 Apr 21 4:18 PM. 11 4 Arithmetic Series 8 April 27, 2009 Apr 21 4:19 PM. 11 4 Arithmetic Series . Homework: page 622 (2 32 even, 37, 40) Title: 11-4 Arithmetic Series Subject: SMART Board Interactive Whiteboard Notes
Unit 11 (Sequences and Series) Day 2: Arithmetic Sequences . 5 The arithmetic mean of any two numbers is the average of two numbers. Some facts: For any three sequential terms in an arithmetic sequence, the middle term is the arithmetic mean of the first and third.
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