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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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