warm up/go over it: 15 minutes announcements: 1 minute homework: 10 minutes geometric sequences: 30...
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WARM UP/GO OVER IT: 15 MINUTESANNOUNCEMENTS: 1 MINUTE
HOMEWORK: 10 MINUTESGEOMETRIC SEQUENCES: 30 MINUTES
CLASS WORK: 20 MINUTESMIDTERM RETURN/CLOSURE: 10 MINUTES
AFM Unit 5 – Sequences and Series
Warm Up
1. Write the explicit and recursive formula for the following sequences:4, 21, 38,… -4.5, -9.5, -14.5,…
2. Find the 6th term of each of the following sequences, and tell whether the formula given is explicit or recursive.
a1 = 10, an = an – 1 – 7 an = 15n – 9
3. Find the common difference of the arithmetic sequence for which a1 = 75 and a38 = 56.5
Announcements
You have until THIS (Friday) afternoon to complete any and all make up work for this quarter. This includes finishing your midterm and make up tests.
I will be here today after school.
You will get your midterm grades back at the end of the period. We will stop about 6 minutes before the bell rings so you can get them back and look through them.
HOMEWORK: Check your answers
1. Yes, d = -3
2. Yes, d = -20
3. Yes, d = -30
4. Yes, d = -10
5. Yes, d = -2
6. Yes, d = 5
7. -4, 3, 10, 17, 24 and 227
8. -35, -135, -235, -335, -435 and -3835
9. -9.2, -11.3, -13.4, -15.5, -17.6 and -63.8
10.1.875, 2.375, 2.875, 3.375, 3.875 and 12.875
Homework – You give ME the answers!
Homework – You give ME the answers!
Homework – You give ME the answers!
Yesterday: Arithmetic Sequences
What do you remember about arithmetic sequences?
What was the formula for the recursive formula?
What was the formula for the explicit formula?
Today: Geometric Sequences
Geometric Sequences – a few examples below to see if you can figure out what makes a geometric sequence a geometric sequence
Geometric Sequence
The ratio between successive terms is constant.
In other words…Each term is multiplied or divided by the same number.
Example: -3, -15, -75, -375
Are the following sequences geometric?
Common Ratio
The number that each term is multiplied or divided by to get the next term.
Represented by the variable “r”To find it: divide any term by the previous
term.Example: What is the common ratio of the
sequence below?
Find the common ratios of the sequences below.
8, -2, 1/2 …
4, 11, 30.25…
W + 3, 2w + 6, 4w + 12…
Find the common ratio and use it to generate the next 4 terms of each sequence below.
- ¼, ½, -1, …
0.5, 0.75, 1.125, …
Recursive Formula
Gives you…The first term (a1)
What to multiply the previous term by
Remember, an – 1 means “the one that came before it”
Geometric Recursive Formula
an = an – 1r
Generate the first 4 terms of the sequences given by the formulas below:
a1 = 8, an = an – 12.5
a1 = 2x, an = an – 15
Recursive Explicit
Let’s say you have a geometric sequence where a1 = 3 and r = 4first term a1 a1 a1 3
Second term
a2
Third term
Fourth term
Fifth term
Sixth term
GEOMETRIC EXPLICIT FORMULA
an = a1 rn – 1
Writing Formulas
Write an explicit and recursive formula for finding the nth term of the geometric sequence below.
2, 25, 312.5,…..
You try the next 3.
36, 12, 4,…
-2, 10, -50,…
4, 8, 16,…
Nth terms
Find the 27th term of the geometric sequence 189, 151.2, 120.96…
You try two.
Find a9 for 60, 30, 15…
Find a6 for 7, 14, 28,…
Arithmetic vs. Geometric
Practice Time
Complete the problems on the worksheet I give you.
You may work with your neighbors.
Whatever you do not finish is homework!
Homework
Finish class work!
Midterm Return
Each part of each question was worth an equal amount.
There was no partial credit. Your answer was either right or wrong.
That means there were 58 total points.Your total correct out of 58 is where I got the
percentage.