1
For each recursive formula, write an explicit formula. For each explicit formula write a recursive formula.
an=3(4)n-1
a1=3, an=4an-1, n ≥ 2
Is the following sequence Arithmetic, Geometric or Neither? 12, 14, 16, 18, 20,.....
Arithmetic
The value of a smartphone depreciates at a rate of 15% per year. If the initial value is $1,000, find the smartphone's value after 3 years. Answer to the Hundredth
$614.125
Find the common difference or ratio to find the next term of the sequence:
-1, -2, -4, -8, __
r= 2
n5= -16
Find the Y-Intercept, Asymptote Domain, Range of f(x)=5x
Y-Intercept:1
Asymptote: 0
Domain: (−∞,∞)
Range: (0,∞) or y>0
What Equation is this?
Y=abx
Exponential Function
For each recursive formula, write an explicit formula. For each explicit formula write a recursive formula.
a1=-2, an=an-1-12, n ≥ 2
an=-12n+10
Is the following sequence Arithmetic, Geometric or Neither? 4, 11, 17, 24, 34,....
neither.
The value of a computer depreciates at a rate of 8% per year. If the initial value is $2,500, find the computer's value after 7 years. Answer to the Hundredth
$1394.62
Find the common difference or ratio to find the next 2 terms in the sequence
0, -4, -8, -12,__, __,...
r= -4
n5= -16
n6= -20
Find the Y-Intercept, Asymptote Domain, Range off(x)=6x -5
Y- Intercept: -4
Asymptote: -5
Domain: (−∞,∞)
Range: (−5,∞) or y> -5
What Equation is this?
y=a(1-r)t
Exponential Decay
For each recursive formula, write an explicit formula. For each explicit formula write a recursive formula.
a1=38, an=(1/2)an-1, n ≥ 2
an=38(1/2)n-1
Is the following sequence Arithmetic, Geometric or Neither? 3, 8, 13, 18, 23,.....
Arithmetic Sequence.
In the year 2000 to 2006, the population of a town decreased by 0.77% annually. In 2001, the population was about 103,931. What is the population of the town in the year 2020
89,735
Find the common difference or ratio to find the next 4 terms of the sequence. Remember how I want the answer.
-1, -0.5, -0.25, -0.125, __, __, __, __,...
r= 1/2
n5= -1/16
n6= -1/32
n7= -1/64
n8= -1/128
Find the Y-Intercept, Asymptote Domain, Range of f(x)=-2x +1
Y-Intercept: 2
Asymptote: 1
Domain: (−∞,∞)
Range: (−∞,1) or y>1
What is the Formulas for Recursive for both Geometric and Arithmetic?
Arithmetic: an=an-1+d
Geometric: an=r*an-1
For each recursive formula, write an explicit formula. For each explicit formula write a recursive formula.
an=-7n+52
a1=45, an=an-1-7, n ≥ 2
Is the following sequence Arithmetic, Geometric or Neither? If so, what is the common difference or common ratio? 500, 460, 420, 380, 340,.....
Arithmetic Sequence with a common difference of -40?
The population of a city is currently 500,000, and it is growing exponentially at a rate of 3% per year. Estimate the population after 20 years. Answer to the Hundredth
903,055.62
Find the first and fifth terms
__, 10, -50, 250, __,...
r= -5
n1= -2
n5= -1,250
Find the Y-Intercept, Asymptote Domain, Range of f(x)=-3x -5
Y-Intercept: -6
Asymptote: -5
Domain: (−∞,∞)
Range: (−∞,-5) or y<-5
What Equation is this?
Y= a(1+r)t
Exponential Growth
For each recursive formula, write an explicit formula. For each explicit formula write a recursive formula.
a1=4, an=an-1+16, n ≥ 2
an=16n-12
Is the following sequence Arithmetic, Geometric or Neither? If so, what is the common difference or common ratio? 3, 15, 75, 375,........
Geometric Sequence with the common ratio of 5?
A swimming pool holds a maximum of water 20,500 gallons of water. It evaporates at the rate of 0.5% per hour. The pool currently contains 19,00 gallons of water.
Write this as a correct equation to express the amount of water remaining in the pool after time (x or t) where time is the number of hours after the pool has reached 19,000 gallons of water.
y= 19,000 (1 - .005)x
Find the first and fourth terms
__, 20, 29, __, 47,...
d= 9
n1= 11
n4= 38
Find the Domain and Range f(x)=-3^(x)+5
Domain: (−∞,∞)
Range: (−∞,5)
What Equation is this? What does each letter mean?
A=P(1+r/n)nt
Compound Interest
A=Current Amount
P= Principal
r=rate
n=number of times per year
t=time