number patterns and sequences 1

8/3/2019 Number Patterns and Sequences 1

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VISHALINI PREMRAJ

KUGAN REDDY

1 ARIF1 ARIF


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Concept Map

Number patterns and SequencesNumber patterns and Sequences

Odd numbers and Even numbersOdd numbers and Even numbers

Prime numbersPrime numbers

FactorsFactors

Prime FactorsPrime Factors

MultiplesMultiples

Common Multiples and Lowest Common MultipleCommon Multiples and Lowest Common Multiple

Common Factors and Highest Common FactorCommon Factors and Highest Common Factor


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Number Sequences

There are patterns all around us. Look at your surroundings. You will see

patterns on walls, windows, doors and so on.

PatternPattern

SequenceSequence


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Pattern

Lines, shapes and objects can be arranged to form a pattern.We can describe the pattern through observation.


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Sequence

List of numbers or objects that follow a certain pattern.We can extend or complete missing terms in a given sequence once we

have identified its pattern.


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Exampl

es

Example 1

Identify the pattern in each of the following.

( a ) 3 , 5 , 7 , 9 , 11 , .

SolutionSolution3 , 5 , 7 , 9 , 11 , .

+2 +2 +2 +2

Pattern : Add 2 to each number.

Sequence : 13


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Example 1


( b ) 6 , 12 , 18 , 24 , 30 , .


+6 +6 +6 +6

Pattern : Add 6 to each number.

Sequence : 36


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Example 2


( a ) 40 , 35 , 30 , 25 , 20 , .


-5 -5 -5 -5

Pattern : Subtract 5 to each number.

Sequence : 15


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Example 2


( b ) 78 , 70 , 62 , 54 , 46 , .


-8 -8 -8 -8

Pattern : Subtract 8 to each number.

Sequence : 38


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Example 3


( a ) 1 , 4 , 16 , 64 , .

SolutionSolution1 , 4 , 16 , 64 , .

x 4 x 4 x 4

Pattern : Multiple 4 to each number.

Sequence : 256


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Example 3


( b ) 6 , 12 , 24 , 48 , 96 , .


x2 x2 x2 x2

Pattern : Multiple 2 to each number.

Sequence : 192


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Odd numbers are whole numbers which

are not divisible by 2.

Examples : 1 , 3 , 5 , 7 , 9 , 11 , ..

Even numbers are whole numbers which

are divisible by 2.Examples : 2 , 4 , 6 , 8 , 10 , 12 , ..

dd Numbers and Even Numbers


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List all the even numbers between

50 and 60.

Answer :

51 , 53 , 55 , 57 , 59


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Prime Numbers

A prime numberprime number is a whole number that

is divisible only by itself and the number1.only by itself and the number1.

Examples :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ..

But, 1 cannot be classified as a prime number.


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All prime numbers are odd numbersexcept 2.

List all the prime numbers between 30 and 50.

31 , 37 , 41 , 43 , 47


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Frequently Asked

PMR Questions


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m , 31 , 37 , 41 , n are five consecutive primenumbers. Find the value ofm +n.

Question 1

A. 70 C. 76

B. 72 D. 90

PMR

2003


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m = 29

n = 43

m + n = 29 + 43

= 72


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A. 70 C. 76

B. 72 D. 90

Question 1PMR

2003

So, the answer is B.

m , 31 , 37 , 41 , n are five consecutive primenumbers. Find the value ofm +n.


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2.42.4 Factors

Factor is a number which divides another number exactly.

The number 1 is a factor of every number.

Every number is a factor of itself.


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ExampleExample

8 1 = 8

8 2 = 4

8 4 = 2

8 8 = 1

The factors of8 are 1 , 2 , 4 and8.


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Prime Factors

Number Patterns and Sequences


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ExampleExample

How many prime numbers are there for 70 ?

Answer

2 70

5 35

7 7

1

Divide the number repeatedly byprime numbers ( starting with the

smallest prime number ) until it is

not divisible.

Therefore, there are 3 prime factors for 70.


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MultiplesMultiples

A multiple of a whole number is the product of

that number and non-zero whole number.

Any number is a multiple of itself. A series of multiples of a number is a sequence.

Example :

5 , 10 , 15 , 20 , 25 ( multiples of 5 ) is a sequences

that is formed by adding 5 to each subsequent number.


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List down the first five multiple of 3.

= 3 x 1 , 2 x 3 , 3 x 3 , 3 x 4 , 3 x 5

= 3 , 6 , 9 , 12 , 15


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2.72.7


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A number which is a multiple of two or morenumbers is called the commonmultiple of these

numbers.

Example :

20 is a multiple of 4.

20 is a multiple of 5.

Therefore, 20 is a common multiple of 4 and 5.

Common Multiple


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The smallest common multiple of two or morenumbers is called theirlowest common

multiple ( LCM ).

Example :

Multiples of 2 = 2 , 4 , 6 , 8 , 10 , 12 , ..

Multiples of 4 = 4 , 8 , 12 , 16 , 20 , 24 , ..

Therefore, the LCM of 2 and 4 is 12.

Lowest Common Multiple ( LCM )


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Alternative MethodAlternative Method

( Algorithm Method )

2 2 , 4

2 1 , 2

3 1 , 1

1 , 1

The LCM of 2 , 4 and 6 is 2 x 2 x 3 = 12


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Frequently Asked

PMR Questions


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Which of the numbers above is not a common

multiple of 3 and 5 ?

Question 1

15 45 55 75

A. 15 C. 55

B. 45 D. 75

PMR

2003


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15 3 = 5

15 5 = 3


45 3 = 15

45 5 = 9



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55 3 = 18 remainder 1

55 5 = 11

Therefore, 55 is NOT a common multiple of 3 and 5.

75 3 = 25

75 5 = 15



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Which of the numbers above is not a common

multiple of 3 and 5 ?

Question 1

15 45 55 75

A. 15 C. 55

B. 45 D. 75

So, the answer is C.

PMR

2003


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2.82.8


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A number which is a factor of two or morenumbers is called the common factorof these

numbers.

Example :Clone PMR 2000 ( Paper 2 Question 7 )

Find all the common factors of 28 and 32.

Factors of 28 = 1 , 2 , 4 , 7 , 14 , 28Factors of 32 = 1 , 2 , 4 , 6 , 8 , 12 , 24

The common factors of 28 and 32 are 1 , 2 and 4.

Common Factor


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The greater common factor of two or morenumbers is called theirhighest common

factor ( HCF ).

Example :

Factors of 8 = 1 , 2 , 4 , 8 , ..

Factors of 24 = 1 , 2 , 4 , 6 , 8 , 12 , ..

The common factors of 8 and 24 are 1 , 2 , 4 and 8.

The HCF of 8 and 24 is 8.

Highest Common Factor ( HCF )


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Alternative MethodAlternative Method

( Algorithm Method )

2 8 , 24

2 4 , 12

2 2 , 6

1 , 3

The HCF of 8 and 24 is 2 x 2 x 2 = 8


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THANK YOUTHE END

number patterns and sequences 1

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