Arithmetic or Geometric & find r or d
2.5 , 3, 3.5, 4, 4.5, ...
Arithmetic: d=0.5
Given the recursive equation
f(1)=20, f(n)=f(n-1)+6, n>=2
Write out the first 4 terms
20, 26, 32, 38, ...
Write an equation for the nth term of the sequence.
108, 36, 12, 4, 4/3...
an = 108(1/3)n-1
The Greek theater has 30 seats in the first row of the center section. Each row behind the first row gains two additional seats.
How many seats are in the 5th row?
There are 38 seats in the 5th row
Write an equation for the nth term of the sequence
3, 8, 13, 18, 23, ...
an = 3 + 5(n-1)
an = 3 + 5n - 5
an = 5n -2
-4, 2, -1, 1/2
Geometric: r=-1/2 or -0.5
Given the sequence f(1)= 7, f(2)=21, f(3)=63, f(4)=189. Find the recursive formula.
f(1)=7, f(n)=3*f(n-1), n>=2
Write an equation for the nth term of the sequence.
1, 4, 7, 10, 13, ...
an = 1 + 3(n-1)
an= 1 + 3n - 3
an = 3n -2
On day 1, 6 students signed up for summer camp. There were 13 students who signed up the next day, then 20 students on the third day and so on.
If the pattern continues, how many students registered on day 8?
55 students
Write an equation for the nth term of the sequence.
3, 15, 75, 375, 1875, ...
an = 3(5)n-1
2, 16, 30, 44...
Arithmetic: d=14
Given the recursive formula:
j(1)=120, j(n)=(1/3)*j(n-1), n>=2
a) Decide if the sequence is geometric or arithmetic
b) Find the nth term of j.
a) geometric
b) j(n)=120(1/3)n-1
Write an equation for the nth term of the sequence.
1, -2, 4, -8, 16, ....
an = 1(-2)n-1
Jose adds paper clips one at a time to an empty envelope. The situation is represented by the eauation: W(n)=7.25+0.5(n-1) , after n paper clips have been added.
Does W(10.25) make sense? Explain how you know.
No, it does not make sense because ...
Write an equation for the nth term of sequence.
-8, -2, 4, 10, 16, ...
an = -8 + 6(n-1)
an = -8 + 6n - 6
an = 6n - 14
-2, -4, -8, -16...
Geometric: r=2
in the table, there are some values of sequence G. Write a recursive definition for the sequence.
*picture*
G(1)=3, G(n)=G(n-1)+4, n>=2
Write an equation for the nth term of the arithmetic sequences. Then find a7.
-6, 1, 8, 15, 22, ...
a7 = -6 + 7(7 - 1)
a7 = -6 + 7(6)
a7 = -6 + 42
a7 = 36
A piece of paper has an area of 80 cm2. A strip is cut off that is 1/2 the original area. From that strip, another strip is cut off that is 1/2 the area of the first, and so on.
a) Create a table that represents this situation
b) Write an equation to define sequence recursively
a) *Table*
b) k(1)=80, k(n)=(1/2)*k(n-1), n>=2
Write an equation for the nth term of the sequence. Then find a8
3, 6, 12, 24, ...
a8 = 3(2)8-1
a8 = 3(2)
a8 = 3(128)
a8 = 384
162, -54, 18, -6, ...
Given the sequence h(1) = 3 and h(2) = 9
If h is a geometric sequence, find the common ratio. Then write an equation to define the sequence recursively. Explain your reasoning.
h(1)=3, h(n)=h(n-1)(3), n>=2
You have an 8in by 10in piece of paper. You are continuously cutting the paper in half. *picture*
What are some values of n that would not make sense in the input?
Explain.
*Varies* examples:
n=1.2
n=-2
n=-0.5
Mr. Carlson suffers from allergies. When allergy season arrives, his doctor recommends that he take 300 mg of his medication the first day, and decrease the dosage by one half each day for one week.
a) Write a "rule" that represents his medication doses for the week?
b) To the nearest milligram, what is the amount of medication Mr. Carlson will take on the 7th day?
a) an=300(1/2)n-1
b) 5 mg (4.6875)
The first two numbers in a sequence h are h(1)=2 and h(2)=8.
If h is an arithmetic sequence, find the common difference. Then write an equation to define the sequence both explicitly. Explain your reasoning.
d= 6
an=2+6(n-1)