Post on 22-Jul-2020
Sequences April 26, 2016
PART ONE !
Warm Up1.) 26, 21, 16, ___, ___, ___, ___
2.) O, T, T, F, F, S, S, E, ____
3.) J, F, M, A, M, J, ____
Find the pattern and fill in the blanks!
Sequences April 26, 2016
Fill in the table values and graph the function at the top of the handout.
When connected, the points create a _________________, which means f(x) is a ____________________ function.
Sequences April 26, 2016
Fill in the table values and graph the following discrete function DO NOT CONNECT THE DOTS!! The notation will look awkward at first. We ask that you treat n like x, and that you treat a like y.
Did you connect the points? What does leaving the points unconnected mean?
What does it mean that there are no points to the left of (1 , 2)?
Sequences April 26, 2016
The equation you graphed is called a discrete function.
Let's look at the avalues that we came up with.
When we look at a list of numbers like this, they are collectively called a sequence. Note that this sequence has a very a very specific starting value (2), but no specified ending value. This is common.
Note also that the points you graphed are linear, and that the terms (numbers) in the sequence are all separated by the same additive value (2). This makes it an arithmetic sequence.
Sequences April 26, 2016
Find the next numbers in the pattern.
4, 9, 14, 19, ____, ____, ____
8, 2, 4, 10, ____, ____, ____
Arithmetic Sequences
Sequence: set of numbers
Term: each number in a sequence
Arithmetic Sequence: each term after the first is found by adding a constant to the previous term
Common Difference (d): constant you add to get next term
***found by subtracting any term by its previous term
Sequences April 26, 2016
an = a1 + (n - 1)dan = term in the sequence
a1 = first term in the sequence
n = # of terms in the sequence
d = common difference
If the first term of the arithmetic sequence is 7 and the common difference equals 3...what is the 279th term?
Do you REALLY want to write out all 279 terms???
Sequences April 26, 2016
Write a rule for the nth term of the arithmetic sequence. Then find a25.
1.) 6, 14, 22, 30, 38 ...
2.) ‐7, ‐3, 1, 5, 9 ...
Write a rule for the arithmetic sequence given ...
3.) a5 = 50 Common Difference = 0.25
4.) a20 = ‐111 Common Difference = ‐6
Sequences April 26, 2016
PART TWO !https://www.youtube.com/watch?v=kkGeOWYOFoA
Warm Up
1.) 4, 16, 64, ___, ___, ___, ___
2.) 32, 16, 8, ___, ___, ___, ___
Sequences April 26, 2016
Fill in the table values and graph the following discrete function
What continuous function does it resemble?
Let's look at the avalues that we came up with.
Again, when we look at a list of numbers like this, they are collectively called a sequence. Note that this sequence has a very a very specific starting value (1), but no specified ending value. Again, this is common.
Sequences April 26, 2016
Note also that the points you graphed are nonlinear, and that the terms (numbers) in the sequence are all not separated by the same additive value. This makes it a geometric sequence.
Example 1: Example 2:
4, 8, 16, 32, _______, _______, _______ 2, 6, 18, 54, _______, _______, _______
Sequences April 26, 2016
Geometric Sequences
Geometric Sequence: each term after the first is found by multiplying a constant to the previous term.
Common Ratio (r): constant you multiply to get next term.
(found by dividing any term by its previous term)
an = a1 r n 1
an = term in the sequence
a1 = first term in the sequence
n = # of terms in the sequence
r = common ratio
GEOMETRIC
SEQUENCE
Sequences April 26, 2016
1.) Write the first six terms of a geometric sequence given:
a1 = 4 & r = 3
____, ____, ____, ____, ____, ____
2.) Write the first six terms of a geometric sequence given:
a1 = 125 & r =
____, ____, ____, ____, ____, ____
25
-
3.) a4 = 10 r = n = 1212
Wrtie the rule and find the nth term for the given geometric sequence.
Sequences April 26, 2016
Write a rule for the nth term of the geometric sequence. Then find a15
4.) 5, 10, 20, 40, ...
a.) Write the rule. b.) Find a15
5.) 6, -30, 150, -750, ...
a.) Write the rule. b.) Find a15