# 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 = 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**

The given series is 32,48,56,60.62 and 63.

The first term : a1 = 32.

2nd term : a1 = 48.

3rd term: a3 = 56.

4th term: a4 = 60.

5th term : a5 = 62

6th term a6 =63.

The increase in sucessiveterms are:

a2-a1 = 16,

a3 -a2 = 56-48 =8.

a4-a3 = 60-56 = 4.

a5-a4 = 62-60 = 2.

a6-a5 = 63-62 = 1.

We notice the the increase of the term s is in a gemeometric ratio, 1/2 .

Therefore increse of a7 over a6 = (1/2) (a6-a5) = (1/2)*1 = 1/2.

Therefore a7 = a6+1/2 = 63+1/2 = 63.5.

So the next term is 63.5.