One of the inherent beauties of mathematics is the logic and order. This logic can be seen “physically” as a pattern or as a series. The mathematician uses patterns to solve problems in geometry as well as in many other fields. In addition, there are some examples of applying finding a pattern strategy in everyday life problem solving situation, such us: searching for an address, the police looks for modus operandi that might lead them to a particular criminal by finding a pattern of crimes, then scientists involved in medical research about the particular virus or bacteria.
More importantly, there are some ways to recognize the pattern in applying the finding a pattern strategy to solve Mathematics problems, they are: (1) different point of view; (2) organizing the data; (3) solving a simpler version; and (4) visual representation.
The following is example of problem in Mathematics solved by finding pattern.
(1) different point of view
Problem: Find the sum of the first 100 even number.
Solution: 2 + 4 + 6 + … + 196 + 198 + 200.
This can be done with calculator, or they can be clever and add in pairs. Recognizing that there is a pattern: 2 + 200 = 202, 4 + 198 = 202, 6 + 196 = 202 and so on. There will be 50 pairs whose sum is 202. Thus, the sum of the first 100 even numbers would be 50 . 202 = 10.100. We also can solve this problem with different point of view.
Number of Even Numbers to be Added 
Sum 

1 2 3 4 . . . n 
22 + 42 + 4 + 62 + 4 + 6 + 8
. . . 2 + 4 + 6 + 8 + … + n 
= 2 = 1 . 2= 6 = 2 . 3= 12 = 3 . 4= 20 = 4 . 5
= n (n + 1) 
So, the sum is 100 . 101 = 10.100
(2) organizing data
Problem:
If you take the digit sum of a number, that is you add the digits in the number, how many three digit numbers will have a digit sum of 10? (For example, 262 is one, since 2 + 6 + 2 = 10; 505 is another, since 5 + 0 + 5 = 10.)
Solution:
We can make use of our organizing data strategy to help set up the lists of numbers with a digit sum of 10 and then see if a pattern exists:
100s: 109, 118, 127, 136, 145, 154, 163, 172, 181, 190 = 10
200s: 208, 217, 226, 235, 244, 253, 262, 271, 280 = 9
300s: 307, 316, 325, 334, 343, 352, 361, 370 = 8
.
.
.
800s: 802, 811, 820 = 3
900s: 901, 910 = 2
Our pattern is confirmed. There are 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 = 54 numbers between 100 and 999 that have a digit sum of 10.
Reference: Posamentier, Alferd S. and Krulik, Stephen. 1998. Problem Solving Strategies for Efficient and Elegant Solution. Corwin Press Inc. California.