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Image Patterns / Shapes Pattern
Number Patterns
Arithmetic or Algebraic Patterns
Example: Complete the following number patterns?
5, 10,15 , __, __, __
First Digit = 5
Second Digit = 5 + 5 = 10
Third Digit = 10 + 5 = 15
Clearly, we will add 5 to the preceding digits respectively to find the rest of the digits.
Fourth Digit = 15 + 5 = 20
Similarly , Fifth Digit = 20 + 5 = 25
Sixth Digit = 25 + 5 = 30
Hence the pattern is 5,10,15,20,25,30.
Geometric Series Pattern
Example: Complete the following number patterns?
10, 100,1000 , __, __, __
First Digit = 10
Second Digit = 10 × 10 = 100
Third Digit = 100 × 10 = 1000
Clearly, we will multiply 10 by the preceding digits respectively to find the rest of the digits.
Fourth Digit = 1000 × 10 = 10000
Similarly , Fifth Digit = 10000 × 10 = 100000
Sixth Digit = 100000 × 10 = 1000000
Hence the pattern is 10,100,1000,10000,100000,1000000.
Fibonacci Pattern
Equal Numbers
Examples 1: Find the missing numbers in the following pattern: 10, 20, _ = 10, _, 15.
As you can see, there are two numbers in the LHS: 10 and 20.
And in RHS: 10 and 15
As there is an equal sign it means both sides will have the same numbers.
So the missing numbers in the LHS = 15
And, the missing number in the RHS = 20
Numbers in LHS: 10, 20, 15
Numbers in RHS: 10, 20, 15
Numbers in LHS = Numbers in RHS
Therefore LHS = RHS
Examples 2. Check whether LHS is equal to RHS: 15+ _ + _ = 30 + 20 + 15 ?
As you can see, there are three numbers in the RHS: 30 + 20 + 15.
And in LHS only 15
As there is an equal sign it means both sides will have the same numbers.
So the missing numbers will be the numbers that are in the RHS i.e, 30 and 20
So, missing numbers in LHS will be 15 + 30 + 20
If you add both LHS and RHS we get,
LHS: 15 + 30 + 20 = 65
RHS: 30 + 20 + 15 = 65
Therefore LHS = RHS
Palindrome
Fun with Odd Numbers
Example 1: Let us find the sum of the first 3 odd numbers.
First 3 odd numbers: 1,3, 5. Here n = 3
Adding 1 + 3 + 5 we get 9.
Also, we know that When we add first n odd numbers,
we will get the sum as n × n.
Sum of first 3 odd numbers = n × n i.e. 3 × 3 = 9
So, the Sum of the first 3 odd numbers is 9.
Example 2: Find the sum of the first 6 odd numbers.
First 6 odd numbers: 1, 3, 5, 7, 9, 11. Here n = 6
Adding 1 + 3 + 5 + 7 + 9 + 11 we get 36.
Also, we know that when we add first n odd numbers,
we will get the sum as n × n.
Sum of first 6 odd numbers = n × n i.e. 6 × 6 = 36
So, the Sum of the first 6 odd numbers is 36.
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