What kind of sequence?
Consider the sequence:
t(n) = 5, 9, 13, 17, ...
Is this sequence arithmetic, geometric, or neither? Why?
Consider the sequence:
t(n) = 5, 9, 13, 17, ...
This is an arithmetic sequence because it always adds by a constant (the common difference). In this case the common difference is 4.
Consider the sequence:
t(n) = 1, 5, 9, 13, 17, ...
A. Find the next three terms.
B. What is the common difference?
C. What is t(0)?
Consider the sequence:
t(n) = 1, 5, 9, 13, 17, ...
A. Find the next three terms: 21, 25, 29
B. What is the common difference? +4
C. What is t(0)? -3
Consider the sequence:
t(n) = 10, 20, 40, 80, ...
A. Find the next three terms.
B. What is the common multiplier?
C. What is t(0)?
Consider the sequence:
t(n) = 10, 20, 40, 80, ...
A. Find the next three terms. 160, 320, 640
B. What is the common multiplier? 2
C. What is t(0)? 5
1. 2x + y = 12 2. y = 3x - 8 3. x = 3y-5
-2x + 3y = 8 y = 2x - 4 2y + x = 10
Methods:
Equal values Substitution Elimination
Match each system of equations below with the best method to solve that system. Do not solve!
1. 2x + y = 12 2. y = 3x - 8 3. x = 3y-5
-2x + 3y = 8 y = 2x - 4 2y + x = 10
Elimination Equal Values Substitution
Consider the sequence:
t(n) = 4,12,36,108,..
Is this sequence arithmetic, geometric, or neither? Why?
The sequence:
t(n) = 4,12,36,108,..
Is geometric because it has a constant multiplier of 3.
Consider the sequence:
t(n) = -15.5, -21, -26.5, -32, ...
A. Find the next three terms.
B. What is the common difference?
C. What is t(0)?
Consider the sequence:
t(n) = -15.5, -21, -26.5, -32, ...
A. Find the next three terms. -37.5, -43, -48.5
B. What is the common difference? -5.5
C. What is t(0)? -10
Consider the sequence:
t(n) = 48, 24, 12, 6, 3, ..
A. Find the next three terms.
B. What is the common multiplier (not common divider)?
C. What is t(0)?
Consider the sequence:
t(n) = 48, 24, 12, 6, 3, ..
A. Find the next three terms. 1.5, .75, .375
B. What is the common multiplier (not common divider)? 1/2 = 0.5
C. What is t(0)? 96
Solve the following system of equations using substitution:
x = 3y - 4
2x + 3y = 19
x = 3y - 4
2x + 3y = 19 --> 2(3y-4) + 3y = 19
--> 9y - 8 = 19 --> 9y = 27 --> y=3
Solution: (5,3) or x=5, y=3
Consider the sequence:
t(n) = 10, 8.7, 7.4, 6.1, ...
Is this sequence arithmetic, geometric, or neither? Why?
The sequence:
t(n) = 10, 8.7, 7.4, 6.1, ...
Is arithmetic because it always adds by a common difference. In this case, the common difference is -1.3.
Consider the sequence:
t(n) = 20, 13, 6, -1, ...
What is the explicit equation for this sequence?
Consider the sequence:
t(n) = 20, 13, 6, -1, ...
What is the explicit equation for this sequence?
t(n) = -7n + 27
Consider the sequence:
t(n) = 20, 80, 320, ...
What is the explicit equation for this sequence?
Consider the sequence:
t(n) = 20, 80, 320, ...
What is the explicit equation for this sequence?
t(n) = 5(4)n
Solve the following system of equations using elimination:
3x - 4y = 18
5x + 4y = -2
3x - 4y = 18
5x + 4y = -2 ---> 8x = 16 --> x = 2
Solution (2,-3) or x=2, y=-3
Consider the sequence:
t(n) = 1215, 405, 135, 45, ...
Is this sequence arithmetic, geometric, or neither? If the sequence is arithmetic, find the common difference (there is no such thing as a common subtracter). If the sequence is geometric, find the common multiplier (there is no such thing as a common divider).
The sequence:
t(n) = 1215, 405, 135, 45, ...
Is geometric. Its common multiplier is 1/3.
Consider the sequence:
t(n) = -8, -1, 6, 13, ...
1. What is the explicit equation for this sequence?
2. Use your explicit equation to find t(38).
Consider the sequence:
t(n) = -8, -1, 6, 13, ...
1. What is the explicit equation for this sequence?
t(n) = 7n-15
2. Use your explicit equation to find t(38).
t(38) = 251
Consider the geometric sequence:
t(n) = 375, 225, 135, 81, ...
What is the explicit equation for this sequence?
Consider the geometric sequence:
t(n) = 375, 225, 135, 81, ...
What is the explicit equation for this sequence?
t(n) = 625(3/5)n = 625(.6)n
Solve the following system of equations using substitution:
x = 8 - 3y
5y - 3x = 32
x = 8 - 3y
5y - 3x = 32 --> 5y - 3(8-3y) = 32
--> 5y - (24-9y) = 32
--> 5y - 24 + 9y = 32
--> 14y = 56 --> y = 4
Solution: (-4,4) or x=-4, y=4
Consider the sequence:
t(n) = 3, 5, 9, 15, 23, ...
The sequence generator is +2, +4, +6, +8, ...
Millie says this is an arithmetic sequence because it is adding and it is adding in a consistent way. Is she correct or not? Why or why not?
The sequence:
t(n) = 3, 5, 9, 15, 23, ...
Is not arithmetic because it does not add by a constant value.
Consider the sequence:
t(n) = 5, 1, -3, -7, ...
1. Find the explicit equation.
2. Use your explicit equation to find n then t(n) = -423
Consider the sequence:
t(n) = 5, 1, -3, -7, ...
1. Find the explicit equation.
t(n) = -4n + 9
2. Use your explicit equation to find n then t(n) = -423
t(108) = -4(108) + 9 = -423, so n=108
Consider the geometric sequence:
t(n) = 900, 300, 100, ...
1. What is the explicit equation for this sequence?
2. Use your explicit equation to find t(10)
Consider the geometric sequence:
t(n) = 900, 300, 100, ...
1. What is the explicit equation for this sequence?
t(n) = 2700(1/3)n
2. Use your explicit equation to find t(10)
t(10) = 2700(1/3)10 = 0.0457...
Solve the following system of equations using elimination:
6x - 5y = 18
15x + 2y = 132
6x - 5y = 18 x5 --> 30x - 25y = 90
15x + 2y = 132 x(-2) --> -30x - 4y = -264
-29y = -174 --> y=6
Solution: (8,6) or x=8, y=6