Arithmetic or Geometric?
-4, 2, -1, 1/2
This is a Geometric sequence
Common ratio: -1/2
-20, -23, -26, -29...
What is -3?
Write the recursive equation
f(n) = 3*2n
f(0)=3, f(n) = f(n-1)*2,n>1
Write an explicit equation for the geometric sequences.
3, 15, 75, 375, 1875, ...
f(n) = 3*5n
Write an explicit equation for the arithmetic sequences.
1, 4, 7, 10, 13, ...
f(n) = 3n +1
A sequence that adds or subtracts the same number every term.
Arithmetic
2 1/2 , 3, 3 1/2, 4, 4 1/2...
What is Arithmetic?
2, 4, 8, 16, 32...
What is times 2 ?
Write the recursive equation
f(n) = -7n+5
f(0) = 5, f(n) = f(n-1)-7, n>=1
Write an explicit equation for geometric sequences.
324, 108, 36, 12, 4, ...
f(n) = 324(1/3)n
Write a recursive equation for the arithmetic sequences.
3, 8, 13, 18, 23, ...
f(1)=3, f(n)=f(n-1)+5, n>=2
The difference between explicit and recursive formulas.
recursive relies on the previous term to find the next term
Explicit does not rely on the previous term
2, 4, 6, 8...
What is Arithmetic?
18, 22, 26, 30...
What is +4?
Write the explicit equation
f(0) = 2, f(n) = f(n-1)*9, n>=1
f(n) = 2*9n
Write an explicit equation for the geometric sequences.
1, -2, 4, -8, 16, ....
f(n)= (-2)n
Write an explicit equation for the arithmetic sequences.
-8, -2, 4, 10, 16, ...
f(n) = 6n - 8
What does the graph of a geometric sequence look like?
Exponential function
3, 9, 27, 81...
What is times 3?
Write the explicit equation
f(0) = 2, f(n) = f(n-1)+9, n>=1
f(n) = 9n+2
Write an explicit equation for the geometric sequences. Then find the 8th term
3, 6, 12, 24, ...
f(n)= 3*(2)n
f(8)= 768
Write a recursive equation for the arithmetic sequences. Then find the 7th term.
-6, 1, 8, 15, 22, ...
f(1)=-6, f(n)=f(n-1)+7, n>=2
f(7)=36
What does the graph of an arithmetic sequence look like?
Straight line (linear function)
The sequence -5, -10, -15, -20
What is what is arithmetic?
The Common Ratio of the Sequence 1000, 200, 40, 8...
What is times 1/5 or divided by 5?
Write the explicit equation
f(0) = -4, f(n) = f(n-1)*-8, n>=1
f(n) = -4*(-8)n
Write an explicit equation for the geometric sequences. Then find the 10th term
128, 64, 32, 16, 8, ...
f(n)= 128(1/2)n
f(10)= 0.125
Write an explicit equation the arithmetic sequences. Find the 10th term
11, 4, -3, -10, -17, -24, ...
f(n) = -7n+11
f(10) = -59
Translate the recursive formula into english
f(1)=10, f(n)=f(n-1)-7, n>=2
The first term is 10. The current term is the previous term minus 7. For all terms after the 1st.