ANALYZING SEQUENCES Practice constructing sequences to model real life scenarios.

43210 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will build a function (linear and exponential) that models a relationship between two quantities. The primary focus will be on arithmetic and geometric sequences. - Linear and exponential functions can be constructed based off a graph, a description of a relationship and an input/output table. - Write explicit rule for a sequence. - Write recursive rule for a sequence. The student will be able to: - Determine if a sequence is arithmetic or geometric. - Use explicit rules to find a specified term (n th ) in the sequence. With help from the teacher, the student has partial success with building a function that models a relationship between two quantities. Even with help, the student has no success understanding building functions to model relationship between two quantities. Focus 7 Learning Goal – (HS.F-BF.A.1, HS.F-BF.A.2, HS.F-LE.A.2, HS.F-IF.A.3) = Students will build a function (linear and exponential) that models a relationship between two quantities. The primary focus will be on arithmetic and geometric sequences.

ROOFING A roofer is nailing shingles to the roof of a house in overlapping rows. There are three shingles in the top row. Since the roof widens from top to bottom, one additional shingle is needed in each successive row. Is this sequence arithmetic or geometric? How do you know? Arithmetic, you add one shingle for each additional row. Write an explicit formula to model this situation. a n = n + 2 Sequence Term Term a1a1 3 a2a2 4 a3a3 5 a4a4 6

ROOFING How many shingles would be in the 7 th row? a 7 = a 7 = 9 Explain at least two ways to find the number of shingles in the fifteenth row. Sequence Term Term a1a1 3 a2a2 4 a3a3 5 a4a4 6

BOUNCING BALL If you ever bounce a ball, you know that when you drop it, it rebounds to the height from which you dropped it. Suppose a ball is dropped from a height of 3 feet and each time it falls, it rebounds to 60% of the height from which it fell. Is this sequence arithmetic or geometric? How do you know? Geometric, you multiply the current height by 0.6 to get the next height.

BOUNCING BALL Write an explicit formula to model this situation. a n = 3(0.6) (n-1) Find the height of the ball after the 4 th rebound. a 4 = 3(0.6) (4-1) a 4 = 3(0.6) 3 a 4 = 3(0.1296) a 4 = feet

MONEY You go to the bank to deposit money and the bank gives you the following two options to choose from. Option A: If you deposit $1000, the second day your account will have $1,100, the third day your account will have $1,200, the fourth day your account will have $1,300, and so forth. Option B: If you deposit $1, the second day your account will have $3, the third day your account will have $9, and the fourth day your account will have $27, and so forth. Without making any calculations, which option do you think gives you more money in 15 days?

Is Option A an arithmetic or geometric sequence? How do you know? Arithmetic, add $100 each day. Is Option B an arithmetic or geometric sequence? How do you know? Geometric, common ratio is $3. Write an explicit formula for Option A. a n = 100n Write an explicit formula for Option B. a n = 1(3) (n-1) Option A: If you deposit $1000, the second day your account will have $1,100, the third day your account will have $1,200, the fourth day your account will have $1,300, and so forth. Option B: If you deposit $1, the second day your account will have $3, the third day your account will have $9, and the fourth day your account will have $27, and so forth.

Option A: a 15 = 100(15) a 15 = a 15 = $2,400 Option A: If you deposit $1000, the second day your account will have $1,100, the third day your account will have $1,200, the fourth day your account will have $1,300, and so forth. a n = 100n Option B: If you deposit $1, the second day your account will have $3, the third day your account will have $9, and the fourth day your account will have $27, and so forth. a n = 1(3) (n-1) Option B: a n = 1(3) (n-1) a 15 = 1(3) (15-1) a 15 = 1(3) (14) a 15 = $4,782,969 Calculate how much money you will have with each option on the 15 th day.