1. Modeling using Sequences
Lesson 4
(Word problems)

2. 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

3. 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

4. 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.

5. 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 = feet

6. 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?

7. Is Option A an arithmetic or geometric sequence? How do you know?
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.
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)

8. Option A: a15 = 100(15) + 900 a15 = 1500 + 900 a15 = $2,400 Option B:
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)
Calculate how much money you will have with each option on the 15th day.
Option A:
a15 = 100(15) + 900
a15 =
a15 = $2,400
Option B:
an = 1(3)(n-1)
a15 = 1(3)(15-1)
a15 = 1(3)(14)
a15 = $4,782,969