Arithmetic
All arithmetic sequences have a __________________
common difference
All geometric sequences have a _________________
common ratio
How old is Panda?
How old is Boo?
Panda - 15
Boo - 4
How many islands make up Hawaii?
8
What element is a diamond made from?
Carbon
A constant difference can be this
positive or negative
Write the explicit and recursive equations for the sequence.
2, 12, 72, 432,...
explicit: f(x) = 2* (6^(x-1))
recursive: f(x) = f(x-1) * 6
Panda needs you to find the missing terms for the following geometric sequence:
4, ___, ___, ___, 324
12, 36, 108
cr = 3
between 0 and 1
0 < cr < 1
1 > cr > 0
$200
Write the explicit and recursive equations for the sequence.
2, -4, -10, -16,...
explicit: f(x) = -6*(x-1)+2
recursive: f(x) = f(x-1) - 6
The first four terms of the sequence are
2, 3, 4.5, 6.75,...
Write recursive and explicit equations for the sequence.
explicit: f(x) = f(x) = 2* (1.5^(x-1))
Boo needs you to find the missing terms for this arithmetic sequence:
4, ___, ___, ___, 324
84, 164, 244
cd = 80
I know the recursive formula and starting point of a sequence is : f(x) = 5*f(x-1) and f(1) = 3
What is the explicit formula?
f(x) = 3 * (5^(x-1))
What is the last word in the Bible?
Amen
An arithmetic sequence has terms f(3) = 10 and f(7) = 26
Find the missing terms between f(3) and f(7) and write an explicit and recursive equation for the sequence.
f(4) = 14
f(5) = 18
f(6) = 22
explicit: f(x) = 4(x-1) + 2
recursive: f(x) = f(x-1) + 4
The first term in a sequence is 12. The sequence decreases by 17% each term. Write the explicit function for this situation. What is the 23rd term in the sequence? (Round to nearest thousandths)
f(x) = 12* (.83^(x-1))
f(23) = 0.199
Boo just landed a great job as an engineer where she will make $65,000 a year. The company she will work for guarantees a 2% pay increase each year so employees’ salaries keep up with inflation. At the end of the year Boo will have made $65,000.
Create an explicit function that represents Boo’s salary.
f(x) = 65,000 (1.02^(x-1))
I know that it is a sequence where f(1) = 5 and the common ratio between terms is 3.
What do you know?
recursive: f(x) = f(x-1) *3
explicit: f(x) = 5*(3^(x-1))
What city was the 1st US Mint constructed in?
Philadelphia
Find the missing terms of the arithmetic sequence represented in the table, and then write the explicit and recursive equations for the sequence.
x 1 2 3 4 5
_______________________________________
y 4 64
cd = 15
recursive: f(x) = f(x-1) + 15
explicit: f(x) = 15* (x-1) + 4
Find the missing terms of the geometric sequence represented in the table, and then write the explicit and recursive equations for the sequence.
x 1 2 3 4 5
_______________________________________
y 4 64
cr = 2
recursive: f(x) = f(x-1) * 2
explicit: f(x) = 4* (2^(x-1))
Panda started a savings account by putting in $25. At the end of the first week, he deposited $15 and plans to continue depositing $15 each week.
Write the recursive and explicit equations for this carless savings practice. (In this economy?)
Also, note starting point is f(0).
recursive: f(x) = f(x-1) + 15
explicit: f(x) = 15*x + 25
I know that the sequence models the value of a car that originally cost $26,500 but loses 10% of its value each year. I also know this sequence starts at f(0).
recursive: f(x) = f(x-1)*.9
explicit: f(x) = 26,500(.9^x)
What is a male duck called?
Drake