WarmUp 11 Thursday 225 Homework Thursday 225 Arithmetic

Warm-Up #11 (Thursday, 2/25) •

Homework Thursday, 2/25 Arithmetic and Geometric Sequences Pg 1 and 2

Arithmetic and Geometric Sequences

Question Every day a radio station asks a question for a prize of $150. If the 5 th caller does not answer correctly, the prize money increased by $150 each day until someone correctly answers their question. • Make for a week (Mon - Fri) if the Daysa list of the prize amounts Amount contest starts on Monday and no one answers correctly all week. Monday Tuesday Wednesday Thursday Friday $150 $300 $450 $600 $750 This is arithmetic sequence because the next term we just add $150

Arithmetic Sequence A sequence in which each term after the first term is found by adding or subtracting a constant, called the common difference (d) to the previous term. Example:

Explanations {150, 300, 450, 600, 750} 1 st term = 150 When x= 1, y= 150 2 nd term = 300 When x= 2, y = 300 f(2) = 300 3 rd term = 450 4 th term = 600 5 th term = 750 f(1) = 150

• Sequence: a list of numbers in a specific order • Term: each number in a sequence

Common difference (notation= d) It is the difference between each number in an arithmetic sequence

Geometric Sequence What if your pay check started at $100 a week and doubled every week. What would your salary be after four weeks? weeks Starting After 1 week After 2 weeks After 3 weeks After 4 weeks Amount $100 $200 $400 $800 $1600

Geometric Sequence A sequence in which each term after the first is found by multiplying or dividing the previous term by a constant value called the common ratio (r) Example:

Explanations 1 st term = 200 When x= 1, y= 200 2 nd term = 400 When x= 2, y = 400 f(2) = 400 3 rd term = 800 4 th term = 1600 0 th term = f(1) = 200

Common ratio (notation = r) It is the ratio of a term to the previous term in a geometric sequence.

Homework Monday, 2/29 • Arithmetic and Geometric Packet • Page 8 #15 -22

Find the next four terms of 0, 7, 14, … and determine the common difference 21, 28, 35, 42 Arithmetic Sequence, d = 7 Find the next four terms of x, 2 x, 3 x, …and determine the common difference 4 x, 5 x, 6 x, 7 x Arithmetic Sequence, d = x Find the next four terms of 5 k, -7 k, …and determine the common difference -13 k, -19 k, -25 k, -32 k Arithmetic Sequence, d = -6 k

Which best describes the sequence 1, 4, 9, 16, …? A. arithmetic B. geometric C. neither

Which best describes the sequence 3, 7, 11, 15, …? A. arithmetic B. geometric C. neither

Which best describes the sequence 1, – 2, 4, – 8, …? A. arithmetic B. geometric C. neither

Find the next three terms in the geometric sequence 2, – 10, 50, …. A. – 50, 250, – 1250 B. – 20, 100, – 40 C. – 250, 1250, – 6250 D. – 250, 500, – 1000

Sequence and Terms Let’s look at the following sequence Do you know what the rule is for the sequence? n² 1, 4, 9, 16, 25, 36, 49, …, The letter a with a subscript is used to represent function values of a sequence. The subscripts identify the location of a term.

How to read the subscripts: the prior term a term in the sequence the next term

Examples • •

Arithmetic Sequence If the sequence is an arithmetic sequence, then it is a linear function with an equation of Explicit formula: y = mx + b Recursive form: Slope y-intercept (starting value) a point (x, y) f(x)= y Common difference f(x)= f(x-1) + d The previous term

Geometric Sequence • growth factor (common ratio) y-intercept (starting value) a point (x, y) Common ratio The previous term

Ex. 1: Find the first four terms of the sequence: General Term Let’s be sure we understand what is given + 2 is The first term is 5 Each term after the first 3 times the previous term Plus 2

Continued… Ex. 1: Find the first four terms of the sequence: Start with general term for n>1 n=1 given n=2 n=3 n=4 Answer = 5, 17, 53, 161

Your turn: Ex 2: Find the next four terms of the sequence. Start with general term for n>1 n=1 given n=2 n=3 n=4 Answer = 3, 6, 12, 24

Try another… n=1 n=2 n=3 n=4 n=5 given = 4– 4=0 = = 0 – 2 = -2 -8 – 0 = -8 Answer = 2, 1, 0, -2, -8

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