WEEK 29-ARITHMETIC-AND-GEOMETRIC-SEQUENCES

Objectives

Start

Arithmetic and Geometric Sequences

1

2

Story

Sequences

Geometric Sequences

Summary

Arithmetic Sequences

Story

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Sequences

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1, 3, 5, 7, ...

×2 ×2 ×2

+2 +2 +2

1

Let's have a look at the following sequences. What is the rule for finding the next term?

1, 2, 4, 8, ...

↺ ↺ ↺

↻ ↻ ↻

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Each next term is found adding 2 to the previous term.

Each next term is found multiplying by 2 the previous term.

1

Generally speaking, a sequence is an ordered list of numbers.

Each number in a sequence is called a term. For instance in our sequence:

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Arithmetic Sequences

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Here:

+3 +3 +3

is the nth term

is the first term

aₙ

a₁

Example 1:

Is an arithmetic sequence with d=+3,a₁=2

2, 5, 8, 11, ...

↺ ↺ ↺

Definition: An arithmetic sequence is a sequence in which the difference between consecutive terms is constant.

is the difference

d

Terms are:

Geometric Sequences and Practice

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Here:

×3 ×3 ×3

is the nth term

is the first term

aₙ

a₁

Example 1:

Is a geometic sequence with r=3,a₁=2

2, 6, 18, 54, ...

↺ ↺ ↺

Definition: A geometric sequence is such that each term after the first is found by multiplying the previous term by a constant.

is the common ratio

r

Terms are:

Try it by yourself:

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Try it by yourself:

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Periodic Savings

Tara saves $100 every month starting with $250. How long until she has $3000?

Sequence:

Click here to draw >

a₁=$250,d=$100, an=$3000, n=?

250, 350, 450,...

Solution

29 months.

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Data follows a positive association.

1.Help yourself writing some terms of the sequence

2. Write the givens

3. Solve for the unknown.

4.

Bacterial Growth

A bacteria culture doubles every hour. If you start with 100 bacteria,

Sequence:

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100, 200,...

Solution

a₁=$100,r=2, n=5, an=?

3200 bacteria

how many will there be after 5 hours?

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1.Help yourself writing some terms of the sequence

2. Write the givens

3. Solve for the unknown.

4.

Arithmetic

geometric

constant Difference of terms

constant quotient of terms

Summary:Sequences

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Welcome 6th graders!

A journey soon begin through Social Science experiences!

Great job!

See you next time

9TH-ARITHMETIC-AND-GEOMETRIC-SEQUENCES-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

"MA.912.AR.10 Write and solve sequence and series equations, functions and inequalities in one and two variables."MA.912.AR.10.1 Given a mathematical or real-world context, write and solve problems involving arithmetic sequences.MA.912.AR.10.2 Given a mathematical or real-world context, write and solve problems involving geometric sequences.ELD.K12.ELL.MA.1 English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.

It is highly advised to have:

MATERIAL

• Grid paper.
• Pencils of different colors.
• Eraser.
• A rule.
• A calculator.
• Geogebra installed on your phone/tablet/computer (or use online version).