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OBJECTIVE We will find the missing terms in an arithmetic and a geometric sequence by looking for a pattern and using the formula.

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**1. 25th term in the sequence 3, 7, 11, 15, 19 …**

Use the formula to find the nth term in an arithmetic sequence. An= A1 + (n-1)d 1. 25th term in the sequence 3, 7, 11, 15, 19 …

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**2. Find the 62nd, 200th, 20th term in the sequence 3, 7, 11, 15, 19 …**

Use the formula to find the nth term in an arithmetic sequence. An= A1 + (n-1)d 2. Find the 62nd, 200th, 20th term in the sequence 3, 7, 11, 15, 19 …

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**3. What is the 47th term in the sequence?**

Use the formula to find the nth term in an arithmetic sequence. An= A1 + (n-1)d 3. What is the 47th term in the sequence? 21, 15, 9, 3, . . .

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**4. What is the 80th term in the sequence?**

Use the formula to find the nth term in an arithmetic sequence. An= A1 + (n-1)d 4. What is the 80th term in the sequence? 21, 15, 9, 3, . . .

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**ARITHMETIC SEQUENCE -is a numerical pattern with a common difference.**

- have an addition or subtraction rule.

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Vocabulary Sequence- a set of numbers {1, 3, 5, 7, …} Terms- each number in a sequence Common Difference- the number added to find the next term of an arithmetic sequence.

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3, 7, 11, 15, 19 … What is the common difference? +4 What is the seventh term in the sequence? 3, 7, 11, 15, 19 , 23, 27

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**look at the PATTERN for the preceding terms**

To find the next term… look at the PATTERN for the preceding terms Ex. 1, 5, 9, ___, ____ Pattern: Add 4

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**FIND the 5th term in the sequence -28, -17, -6, 5…**

Find the common difference by subtracting the 2nd term and the 1st term: +11 Add 11 to the 4th term in the sequence: = 16 ANSWER: The 5th term is 16

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**FIND the 10th term in the sequence -28, -17, -6, 5…**

Find the common difference by subtracting the 2nd term and the 1st term: +11 Add 11 from the 4th to the 10th term in the sequence: -28, -17, -6, 5, 16, 27, 38, 49, 60, 71 ANSWER: The 10th term is 71

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GEOMETRIC SEQUENCE The ratio of successive terms in a geometric sequence is a constant called the common ratio, denoted by r.

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**Find the common ratio and the 8th term of the following:**

1) 1, 2, 4, 8, 16, ... 2) 27, 9, 3, 1, 1/3, ... 3) 3, 6, 12, 24, 48, ... 4) 1/2, -1, 2, -4, 8, ...

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**This is important! Arithmetic formula: **

an = a1 + (n - 1)d an is the nth term, a1 is the first term, and d is the common difference. Geometric formula: an = a1 . r (n - 1) an is the nth term, a1 is the first term, and r is the common ratio.

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**Let's play guess the sequence!: I give you a **

sequence and you guess the type. 3, 8, 13, 18, 23, . . . 1, 2, 4, 8, 16, . . . 24, 12, 6, 3, 3/2, 3/4, . . . 55, 51, 47, 43, 39, 35, . . . 2, 5, 10, 17, . . . 1, 4, 9, 16, 25, 36, . . .

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**Answers! 1) Arithmetic, the common difference d = 5**

2) Geometric, the common ratio r = 2 3) Geometric, r = 1/2 4) Arithmetic, d = -4 5) Neither, why? (How about no common difference or ratio!) 6) Neither again! (This looks familiar, could it be from geometry?)

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**Sample problems: 1) an = 3n + 2 2) an = n2 + 1 3) an = 3*2n **

Find the first four terms and state whether the sequence is arithmetic, geometric, or neither. 1) an = 3n + 2 2) an = n2 + 1 3) an = 3*2n

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Arithmetic and Geometric Sequences. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 1. 7, 13, 19, 25, …2.

Arithmetic and Geometric Sequences. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 1. 7, 13, 19, 25, …2.

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