ANALYZING SEQUENCES

Practice constructing sequences to model real life scenarios.

4 3 2 1 0In 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 (nth) in the sequence.  

With help from theteacher, the student haspartial 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.

an = n + 2

Sequence Term

Term

a1 3

a2 4

a3 5

a4 6

ROOFING

How many shingles would be in the 7th row?

a7 = 7 + 2

a7 = 9

Explain at least two ways to find the number of shingles in the fifteenth row.

Sequence Term

Term

a1 3

a2 4

a3 5

a4 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.

an = 3(0.6)(n-1)

Find the height of the ball after the 4th rebound.

a4 = 3(0.6)(4-1)

a4 = 3(0.6)3

a4 = 3(0.1296)

a4 = 0.3888 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.

an = 100n + 900

Write an explicit formula for Option B.

an = 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:

a15 = 100(15) + 900

a15 = 1500 + 900

a15 = $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.an = 100n + 900

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.an = 1(3)(n-1)

Option B:an = 1(3)(n-1)

a15 = 1(3)(15-1)

a15 = 1(3)(14)

a15 = $4,782,969

Calculate how much money you will have with each option on the 15th day.