HOW TO PATTERN MODEL FROM GIVEN TABLE

For the following input numbers and output numbers, find the rule in the number crunching machine :

Example 1 :

Solution :

By observing the output values each values is consecutive multiples of 3.

Let x and y be input and output values respectively.

By following rule, we get

So, the required rule is M  =  3n

Example 2 :

Solution :

Let x and y be the input and output values respectively.

By observing the output values each values is consecutive odd integers starts with 3.

Multiple of 2 nearest to 3 are 2 and 4.

2x is the even number, to get 3 we add 1 with 2x.

4x is also even number, to get 3 we should subtract 1 from 4x. So, the general term may be 4x-1.

Since it is not working when the inputs are 2, 3 and so on. So, we choose 2x+1.

So, the required rule is M  =  2n+1

Example 3  :

Solution :

By observing the output values each values is odd numbers, but it starts with 7.

By following rule, we get

So, the required rule is M  =  2n+5.

Example 4  :

Solution :

The outputs are not consecutive. The even number nearest to 5 is 4.  To create a multiple of 4, we use 4x+1.

By following rule, we get

So, the required rule is M  =  4n+1.

Example 5 :

Solution :

Difference of each consecutive terms is 5. So, let us fix multiple of 5.

To get multiple of 5, we use 5x.

First term is multiple of 5 but it is less than 2.So, the general term is 5x-2.

So, the required rule is M  =  5n-2.

Example 6 :

The difference of each consecutive terms is 3.

So, let us use 3x to get multiples of 3. To get 7 we should use 3x+4.

So, the required formula is M  =  3n+4.

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