What is the next number in this pattern:32, 48, 56, 60, 62, 63,...

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Let the missing number be x:

32, 48, 56, 60, 62, 63, x

We will find the difference between terms in order to find a common ratio :

==> 48 - 32 = 16

==> 56 - 48 =  8

==> 60 - 56 = 4

==> 62 - 60...

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Let the missing number be x:

32, 48, 56, 60, 62, 63, x

We will find the difference between terms in order to find a common ratio :

==> 48 - 32 = 16

==> 56 - 48 =  8

==> 60 - 56 = 4

==> 62 - 60 = 2

==> 63 - 62= 1

==> x - 63 = ?

We notice that there is a pattern for the difference between each two consecutive terms.

The sequence of the differences s:

16, 8, 4, 2, 1, ...

Then we notice that the differences sequence is a geometric progression such that: r = 1/2

Then the last difference will be 1*1/2 = 1/2

Then the difference between the last two terms = 1/2

==> x - 63 = 1/2

==> x = 63.5

Then the missing number is 63.5

 

 

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