Download Recursive Worksheet

Recursive Patterns
Fill in these two columns:
#
Numbers
Start
Explanation in Words
Explanation
with Next/Now
Algebraic
Notation
1
8, 5, 2, -1…
8
Subtract 3
NEXT = NOW - 3
2
12, 6, 3, 3/2…
12
Multiply by ½
Or Divide by 2
NEXT = NOW * ½
NEXT = NOW / 2
V1 = 8
Vn+1= Vn - 3
V1 = 12
Vn+1 =(1/2) Vn
Or Vn+1 =Vn /2
3
5, 11, 17, 23, 29…
4
½, 3/2, 9/2, 27/2
5
7, 2, -3, -8 ….
These patterns can also be written as NEXT = NOW * #
Or NEXT = NOW + #
Example: 7, 10, 13 can be written as NEXT = NOW + 3
Fill in this column
START can be written as V1
NOW can be written as Vn
NEXT can be written as Vn+1
So 7, 10, 13… can be written as
V1 = 7;
Vn+1 = Vn + 3
Fill in this column
Now fill in the chart below.
#
Algebraic
START
6
V1 = 7
7
Explanation with
Explanation in
NEXT/NOW
words
NEXT = NOW - 3
Subtract 3
Vn+1 = Vn - 3
7
P1 = 24
Pn+1 = (1/3) Pn+1
8
T1 = 54
Tn+1 = Tn + 1.5
9
V1 = 20,000
Vn+1 = 1.04(Vn)
10
11
16
X
Y
0
7
1
12
2
17
3
22
NEXT = NOW/4
First four terms
V1 = 7
V2 = 4
V3 = 1
V4 = -2
Recursive Patterns
increase 5% means to multiply by 1.05
Vn+1 = 1.05 Vn
increase 4.3% means to multiply by 1.043
Vn+1 = 1.043 Vn
increase 8% means to multiply by _____
Vn+1 =
increase ____ means to multiply by 1.035
Vn+1 =
decrease 7% means to multiply by .93
Vn+1 = .93 Vn
decrease 12% means to multiply by .88
Vn+1 =
decrease 5% means to multiply by ___
Vn+1 =
decrease _____ means to multiply by .75
Vn+1 =
12) Write the recursive equation that models a house appreciating by 5% every year if the original price was
$140,000.
13) Write the recursive equation that models a $15,000 car depreciating by 12.5% yearly.
Answer the following recursive equations
14) A cyclist starts 84 miles from his home. Each hour he rides brings him 12 miles closer to his
home.
A) Write a recursive equation that represents the distance he is from his home.
START = 84. NEXT = NOW – 12
D1 = 84; Dn+1 = Dn – 12
B) Find out how far he is from his own after each hour.
D1 = 84
D2 = 84 – 12 = 72
D3 = 72 – 12 = 60
D5 =
D6 =
=
D7 =
=
C) How many hours does it take him to reach his house?
D4 = 60 – 12 = 48
D8 =
=0
8 hours since D8 = 0
15) The balance of a bank account that earns 2% a year can be defined as NEXT = NOW +
0.02*NOW or as NEXT = NOW * 1.02. Jack puts $100 at the end of the first year.
A) Write a recursive equation that represents this situation. B) Find out how much he has after each year for 10 years.
16) The value of a car depreciates by 15% a year.
It can be defined algebraically as Vn+1 = (.85)Vn. V1 = $20,000
A) What is the START VALUE at the end of the first year?
B) Write the NEXT/NOW equation.
C) How much is the car worth at the end of 7 years?
17) A ball’s height can be represented as Hn+1 = (.6)Hn where Hn+1 is the height and Hn is the
previous height.
A) How high does the ball go from the previous height?
B) If the height after the 4th bounce is 3ft, how high is it after the 7th bounce?