Presentation is loading. Please wait.

Presentation is loading. Please wait.

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

Similar presentations


Presentation on theme: "OBJECTIVE We will find the missing terms in an arithmetic and a geometric sequence by looking for a pattern and using the formula."— Presentation transcript:

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

2 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 …

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

4 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,...

5 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,...

6 ARITHMETIC SEQUENCE -is a numerical pattern with a common difference. - have an addition or subtraction rule.

7 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.

8 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

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

10 FIND the 5 th term in the sequence -28, -17, -6, 5… 1.Find the common difference by subtracting the 2 nd term and the 1 st term: Add 11 to the 4 th term in the sequence: = 16 ANSWER: The 5 th term is 16

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

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

13 Find the common ratio and the 8 th 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,...

14 This is important! Arithmetic formula: a n = a 1 + (n - 1)d a n is the nth term, a 1 is the first term, and d is the common difference. Geometric formula: a n = a 1. r (n - 1) a n is the nth term, a 1 is the first term, and r is the common ratio.

15 Let's play guess the sequence!: I give you a sequence and you guess the type. 1.3, 8, 13, 18, 23, , 2, 4, 8, 16, , 12, 6, 3, 3/2, 3/4, , 51, 47, 43, 39, 35, , 5, 10, 17, , 4, 9, 16, 25, 36,...

16 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?)

17 Sample problems: Find the first four terms and state whether the sequence is arithmetic, geometric, or neither. 1) a n = 3n + 2 2) a n = n ) a n = 3*2 n

18


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

Similar presentations


Ads by Google