Explicit Equation
What is the common difference in the following equation?
t(n) = 7n - 5d = 5
Finish the phrase:
To get the next term…
… you take the term before it, and something happens”
Bonus: What is this in symbols?
Sequences always start on...
Term 1
t(1)
x4 * x5
x9
Is the following sequence increasing or decreasing? How do you know?
t(n) = 6 * 2n
Increasing because the multiplier is x2
Write the recursive equation for the following sequence:
18, 26, 34, 42...
t(n+1) = t(n) + 8, t(0) = 10
What is t(3) of the sequence below
3, 7, 11, 15...
t(3) = 11
Simplify:
4(x + 2) = 20
x = 3
Write the explicit equation for the following sequence:
8, 13, 18, 23…
t(n) = 5n + 3
Why is the following incorrect?
t(n + 1) = t(n) * 4, t(0) = 2
2, 8, 32, 128...
t(0) = 2, but in the sequence is written with t(1) = 2.
Sketch an example of what the graph of an arithmetic sequence would look like
Bonus for 100: Why don't you connect the dots?
(x + 2) (x + 7)
x2 + 9x + 14
What is the explicit equation for the following sequence?
4, 20, 100, 500…
t(n) = 0.8 * 5n
Write the recursive equation for the following sequence:
4, 24, 144, 864...
t(n+1) = t(n) * 6, t(0) = 0.66
or
t(n+1) = t(n) * 6, t(1) =4
The domain of sequences is...
Positive Integers Greater than 1
(1, 2, 3, 4...)
What is the definition of a function?
Is a sequence a function?
For every input, there is one and only one output
Yes, all sequences are functions
What is the explicit equation for the following sequence?
100, 50, 25, 12.5…t(n) = 200 *(0.5)n
Explain in words why you have to give a term for a recursive equation.
A recursive equation tells you how to get the next term given a previous term, but without "giving a term", you can create an infinite amount of sequences with the same growth/sequence generator.
Why is this equation wrong?
10, 15, 20, 25...
t(n) = 5n +t(5)
t(0) = 5, and they represented this as t(5), which means "Term Number 5".
With Explicit Equations you "replace"
With Recursive Equations you "tell"
What is the domain and range of the provided graph?
See Board