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
Identify the pattern in each of the following.
( b ) 6 , 12 , 18 , 24 , 30 , .
SolutionSolution6 , 12 , 18 , 24 , 30 , .
+6 +6 +6 +6
Pattern : Add 6 to each number.
Sequence : 36
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Example 2
Identify the pattern in each of the following.
( a ) 40 , 35 , 30 , 25 , 20 , .
SolutionSolution40 , 35 , 30 , 25 , 20 , .
-5 -5 -5 -5
Pattern : Subtract 5 to each number.
Sequence : 15
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Example 2
Identify the pattern in each of the following.
( b ) 78 , 70 , 62 , 54 , 46 , .
SolutionSolution78 , 70 , 62 , 54 , 46 , .
-8 -8 -8 -8
Pattern : Subtract 8 to each number.
Sequence : 38
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Example 3
Identify the pattern in each of the following.
( 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
Identify the pattern in each of the following.
( b ) 6 , 12 , 24 , 48 , 96 , .
SolutionSolution6 , 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
Therefore, 15 is a common multiple of 3 and 5.
45 3 = 15
45 5 = 9
Therefore, 45 is a common multiple of 3 and 5.
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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
Therefore, 45 is a common multiple of 3 and 5.
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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