12.2, 12.3: Analyze Arithmetic and Geometric Sequences HW: p (4, 10, 12, 18, 24, 36, 50) p (12, 16, 24, 28, 36, 42, 60)

 In an arithmetic sequence, the difference of consecutive terms is constant. This difference is called the common difference and is denoted by d.  Tell whether the sequence is arithmetic:  -4, 1, 6, 11, 16, …  3, 5, 9, 15, 23, …

The nth term of an arithmetic sequence with first term a 1 and common difference d is given by: a n = a 1 + (n – 1)d This is an explicit rule because it gives a n as a function of the term’s position number n in the sequence. What is another way to express this rule?

1.) 4, 9, 14, 19, … 2.) 60, 52, 44, 36, …

1.) One term of an arithmetic sequence is a 19 = 48. The common difference is d = 3. a.) Write a rule. b.) Graph the sequence. 2.) Two terms of an arithmetic sequence is a 8 = 21 and a 27 = 97. Write a rule.

12.2, 12.3: Analyze Arithmetic and Geometric Sequences HW: p (4, 10, 12, 18, 24, 36, 50) p (12, 16, 24, 28, 36, 42, 60)

 In a geometric sequence, the ratio of any term to the previous term is constant. This constant ratio is called the common ratio and is denoted by r.  Tell whether the sequence is geometric:  4, 10, 18, 28, 40, …  625, 125, 25, 5, 1, …

The nth term of a geometric sequence with first term a 1 and common ratio r is given by: a n = a 1 r n-1 This is an explicit rule because it gives a n as a function of the term’s position number n in the sequence. Write a rule for the nth term of the sequence. Then find a 7. 1.) 4, 20, 100, 500, … 2.) 152, -76, 38, -19, …

1.) One term of a geometric sequence is a 4 = 12. The common ratio is r = 2. a.) Write a rule. b.) Graph the sequence. 2.) Two terms of an geometric sequence is a 3 = -48 and a 6 = Write a rule.