We can think of a pattern as a design or picture which repeats itself at regular intervals.

The simplest pattern is the set {0, 1, 2, 3, 4, ....} where one is added each time.
0, (0+1=1), (1+1=2), (2+1=3), ....

To solve number patterns, examine the differences between numbers and try to find a pattern.
 

Now look at the horizontal numbers in the red blocks below {4, 8, 12, 16, 20} .
The numbers are increased by four forming the pattern. We can look at the pattern as an addition or multiplication (multiplication is just a form of addition).
eg. (0+4=4), (4+4=8), (8+4=12), ....  or (1*4=4), (2*4=8), (3*4=12), .....
Now observe the vertical numbers in the pink blocks (7, 14, 21, 28, 35l ......) and find the pattern.

The diagonal numbers in the blue blocks {1,4,9,16,25, .....} form a more complicated pattern.
In the first case 3 is added to 1, then 5 is added to four, then 7 and so on forming the following pattern: (1+3 = 4), (4+5 = 9), (9+7 = 16), (16+9 = 25) .......
We can now predict what comes next since 3, 5, 7, 9 ... has a pattern where the number is increased by 2 each time, hence 11 is the next number to be added after 9 (9+2=11), and 25 + 11 = 36.

In the other set of diagonal numbers in the green blocks, the number which is added is decreasing. Can you find that number and hence figure out the pattern ?
 

Observe The
Patterns