Warm-up L11-2 & L11-3 Obj: Students will be able to find the general term for arithmetic series.

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Warm-up L11-2 & L11-3 Obj: Students will be able to find the general term for arithmetic series

Is the given sequence arithmetic? Arithmetic Sequences LESSON 11-2 Additional Examples Is the given sequence arithmetic? a. 7, 10, 13, 16, . . . b. The sequence of dots in the “triangles” shown below.

Practice

Write a recursive and explicit formula for each sequence Find the 30th term for each A. 34, 37, 40, 43,… B. 0.1, 0.5, 0.9, 1.3,…

Arithmetic Sequences LESSON 11-2 Additional Examples Suppose you have already saved $75 toward the purchase of a new CD player and speakers. You plan to save at least $12 a week from money you earn at a part-time job. In all, what is the minimum amount you will have after 26 weeks?

Write an explicit formula for the following sequence: 2 7 12 17 Find the 24th term Write a recursive formula for the following sequence: 21 18 15 12 Find the next three terms

Find the missing term of the arithmetic sequence 50, , 92.

Practice 1. -16, ___, 1 2. 5, ___, 21 3. 101, _____, -115 4. 2,___, ___,___,-22 5. 1,___, ___,___,-35 6. -17, ___,___,___,1

Obj: Students will be able to identify and generate geometric sequences

Find the next two terms 1. 1,2,4,8,… 2. 1,-2,4,-8,… 3. 10,4,1.6,.64,… Practice Find the next two terms 1. 1,2,4,8,… 2. 1,-2,4,-8,… 3. 10,4,1.6,.64,…

1. Find the explicit formula for each sequence 1. Find the explicit formula for each sequence. Then generate the first 4 terms. a1= 3, r = -2 2. Find the explicit formula for each sequence. Find the recursive formula for each sequence. Then generate the first 4 terms. a1= -1, r = 4

Practice a. Find the explicit formula for each sequence. b. Find the recursive formula for each sequence c. Then generate the first 4 terms. 1. a1 = 32, r = -.05 2. a1 = 9, r = 2

Ex: Find the missing term 1. -1, ___, -36 2. 12.5, ___, ___, ___, 5.12

Ex: Find the missing term 1. -1, ___, -36 2. 12.5, ___, ___, ___, 5.12

Geometric Sequences LESSON 11-3 Additional Examples Suppose you have equipment that can enlarge a photo to 120% of its original size. A photo has a length of 10 cm. Find the length of the photo after 5 enlargements at 120%. You need to find the 6th term of the geometric sequence 10, 12, 14.4, . . .

geometric mean = 150,000 • 188,160 Use the definition. Geometric Sequences LESSON 11-3 Additional Examples A family purchased a home for $150,000. Two years later the home was valued at $188,160. If the value of the home is increasing geometrically, how much was the home worth after one year? geometric mean = 150,000 • 188,160 Use the definition. = 28,224,000,000 Multiply. = 168,000 Take the square root. Homework: L11-2 (p. 618) #16-40e 48-56e 64, 66 L11-3 (p. 625 #14-30e 38-52e