GENERATES PATTERNS

GENERATES PATTERNS

by Michelle Mae Malificiado

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​The module is divided into four lessons, namely:

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•· Lesson 1 – Patterns and Sequence

•· Lesson 2 – Explicit Form of Sequence

•· Lesson 3 – Recursive form of Sequence

​OBJECTIVES:

​1. solve and generate patterns;

2. solve sequence using explicit form of sequence;

3. solve sequence using recursive form of sequence

​What is next?

1. 70, 60, 50, ___, ___, ___

2. 77, 102, 127, ___, ___

3. 134, 125, ___, ___

4. 121, 129, 137, ___, ___

5. 638, 538, 438, ___, ___

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​6. 59, 70, 81, ___, ___

7. 90, 84, 78, ___, ___

8. 78, 85, 92, 99, ___, ___

9. 159, 147, ___, ___

10. 76, 91, 106, ___, ___

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​ANSWER:

1. 70, 60, 50, 40, 30

2. 77, 102, 127, 152, 177

3. 134, 125, 116, 107

4. 121, 129, 137, 145, 153

5. 638, 538, 438, 338, 238

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​6. 59, 70, 81, 92, 103

7. 90, 84, 78, 72, 66

8. 78, 85, 92, 99, 106, 113

9. 159, 147, 135, 123

10. 76, 91, 106, 121, 136

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LESSON 1: ​

Patterns and Sequences​

​WHAT’S IN 

​•A pattern is an arrangement of things repeated in an orderly, recognizable fashion.

Example :

What is the next figure in the pattern below?

​WHAT’S IN 

​•A pattern is an arrangement of things repeated in an orderly, recognizable fashion.

Example :

What is the next figure in the pattern below?

​WHAT’S NEW

​An ordered list of numbers such as 2, 5, 8, 11,14,… is called a sequence.

The numbers in a sequence, that are separated by commas, are the terms of the sequence.2, 5, 8, 11,14, ...

2 is the first term

5 is the second term

8 is the third term

11 is the fourth term

14 is the fifth term

The three dots “… ” indicate that the sequence continues beyond 14, which is the last written.

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​Numbers in a problem that are not given can be found by using established pattern.

Example 

What number comes next in 1,3,5,7,9,_____ ?

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​Numbers in a problem that are not given can be found by using established pattern.

Example 

What number comes next in 1,3,5,7,9,_11_ ?

​WHAT’S NEW

​An ordered list of numbers such as 2, 5, 8, 11,14,… is called a sequence.

The numbers in a sequence, that are separated by commas, are the terms of the sequence.2, 5, 8, 11,14, ...

2 is the first term

5 is the second term

8 is the third term

11 is the fourth term

14 is the fifth term

The three dots “… ” indicate that the sequence continues beyond 14, which is the last written.

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​•Sn = a1, a2, a3, a4, a5 ,…

Where:

•a1 represent the first term of the sequence

•a2 represents the second term of a sequence

•a3 represents the third term of a sequence.

•an represents the nth term of a sequence.

​Sequence

• It is a succession of numbers in specific orders.

• Each number in a sequence is called term.

• The terms are formed according to some fixed rule or property.

• They are arranged as the first term, the second term, the third term, and so on.

  * A sequence with a definite number of terms is a finite sequence.

*In a finite sequence, the first and the last are clearly identified

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​NOTE:

​•Each of the number in the sequence is called a term.

•In order to find the missing terms in a number sequence, we must first find the pattern of the number sequence.

​Explicit Form of a Sequence

• It is sequence that can be expressed in a form in which a preceding term is not necessary to find the succeeding terms.

• This explicit form can be used can be used to find term of the sequence by determining its position.

​EXPLICIT FORM OF SEQUENCE.

​What is the 10th term in the sequence

  2, 6, 12, 20, 30, n² + n…? 

Solution:

From the sequence,

a1=2, a2=6, a3=12, a4=20, a5=30, and an = n² + n

•Hence, the 10th term is a10 = 10² +10 = 110.

​Example: Write the explicit form

​For the sequence 5, 8, 11, 14,.. find the next two sequence.

Solution:

a1 = 5 = 3(1) + 2

a2 = 8 = 3(2) + 2

a3 = 11 = 3(3) + 2

a4= 14 = 3(4) + 2

The explicit for of the sequence is an = 3n + 2 ; The next two terms are: a5 = 3(5) +2 = 15 + 2 = 17 a6 = 3(6) +2 = 18 + 2 = 20

​Recursive Form of a Sequence

• It is a sequence if the first term and a recursive formula are given.

  A recursive formula is an expression used to determine the nth term of the sequence by using the term that precedes it.

​Recursive Form of a Sequence

​another way of examining the next term the nth term formula is by constructing a difference table.

Example: 3, 9, 15, 21 ...

​​​sequence

​​first difference

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​GOOD LUCK AND GOD BLESS​!