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4-1 Using Graphs to Relate Two Quantities

Objectives: To identify and extend patterns in sequences. To represent arithmetic sequences using functions notationSection 4-7

Arithmetic SequencesWarm up:

A wooden post-and-rail fence with two rails is made as shown. Find the number of pieces of wood needed to build a 4-section fence, a 5 section fence, and a 6-section fence. Suppose you want to build a fence with 3 rails. How many pieces of wood are needed for each size fence? Describe the pattern.Key VocabularySequence: an ordered list of numbers that often form a pattern.

Term of a Sequence: Each number in the list

Problem #1: Extending SequencesDescribe a pattern in each sequence. What are the next two terms of each sequence?A)

B)

Problem #1Got It?Describe a pattern in each sequence. What are the next two terms of each sequence.

5, 11, 17, 23,

400, 200, 100, 50,

2, -4, 8, -16,

-15, -11, -7, -3, More VocabularyArithmetic Sequence: A number sequence formed by adding a fixed number to each previous term to find the next.

Common Difference: The fixed number added to each previous term in an Arithmetic Sequence

Problem #2: Identifying an Arithmetic SequenceTell whether the sequence is arithmetic. If it is, what is the common difference?A)3, 8, 13, 18, B)-3, -7, -10, -14, Problem #2Got It?Tell whether each sequence is arithmetic. If it is, what is the common difference?

8, 15, 22, 30,

7, 9, 11, 13,

10, 4, -2, -8,

2, -2, 2, -2, More VocabularyRecursive Formula: A function rule that relates each term of a sequence after the first to the ones before itConsider the sequence 7, 11, 15, 19

Consider the sequence 7, 11, 15, 19

Common Difference:

Problem #3: Writing a Recursive FormulaA) Write a recursive formula for the arithmetic sequence below. What is the value of the 8th term?70, 77, 84, 91,Problem #3: Writing a Recursive FormulaB) Write a recursive formula for the arithmetic sequence below. What is the value of the 7th term?3, 9, 15, 21Problem #3Got It?Write a recursive formula for each arithmetic sequence. What is the 9th term of each sequence?

23, 35, 47, 59,

7.3, 7.8, 8.3, 8.8,

97, 88, 79, 70, HomeworkTextbook Page 279; #10 34 Even Objectives: To represent arithmetic sequences using functions notationSection 4-7

ContinuedKey VocabularyExplicit Formula: A function rule that relates each term of a sequence to the term number

The nth term of an arithmetic sequence with first term A(1) and common difference d is given by:7, 11, 15, 19,

Problem #4: Writing an Explicit FormulaA) An online auction works as shown below. Write an explicit formula to represent the bids as an arithmetic sequence. What is the 12th bid?

Problem #4: Writing an Explicit FormulaB) A subway pass has a starting value of $100. After one ride, the value of the pass is $98.25. After two rides, its value is $96.50. After three rides, its value is $94.75. Write an explicit formula to represent the remaining value on the card as an arithmetic sequence. What is the value of the pass after 15 rides?

Problem #4: Writing an Explicit FormulaC) Using your answer from B, how many rides can be taken with the $100 pass?

Problem #4Got It?Justines grandfather puts $100 in a savings account for her on her first birthday. He puts $125, $150, and $175 into the account on her next 3 birthdays. If this pattern continues, how much will Justines grandfather put in the savings account on her 12th birthday?22Problem #5: Writing an Explicit Formula From a Recursive FormulaA) An arithmetic sequence is represented by the recursive formula A(n)=A(n 1) + 12. If the first term of the sequence is 19, write the explicit formula.Problem #5: Writing an Explicit Formula From a Recursive FormulaB) An arithmetic sequence is represented by the recursive formula A(n)=A(n 1) + 2. If the first term of the sequence is 21, write the explicit formula.Problem #5Got It?An arithmetic sequence is represented by the recursive formula A(n)=A(n 1) + 7. If the first term of the sequence is 2, write the explicit formula.25Problem #6: Writing a Recursive Formula From an Explicit FormulaA) An arithmetic sequence is represented by the explicit formula A(n)= 32 + (n 1)(22). What is the recursive formula?Problem #6: Writing a Recursive Formula From an Explicit FormulaB) An arithmetic sequence is represented by the explicit formula A(n)= 76 + (n 1)(10). What is the recursive formula?Problem #6Got It?An arithmetic sequence is represented by the explicit formula A(n)=1 +(n 1)(3). Write the recursive formula.28HomeworkTextbook Page 278 280; #1 8, 36 52 Even