warm up/go over it: 15 minutes announcements: 1 minute homework: 10 minutes geometric sequences: 30...

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.