# How to Solve Civil Service Exam Number Series Problems 4

This is the fourth part of the solving number series problems. The **first part** discussed patterns that contains addition and subtraction and the **second part** discusses patterns that contains multiplication or division. The **third part** was about alternating patterns.

In this post, we are going to discuss some special number patterns. Although there is a small probability that these types of patterns will appear in the Civil Service Examination (I didn’t see any when I took the exams, both professional and subprofessional), it is better that you know that such patterns exist.

**Triangular Numbers**

1, 3, 6, 10, 15, 21, 28, 36, 45, …

Triangular numbers are numbers that are formed by arranging dots in triangular patterns. Therefore, the first term is 1, the second term is 1 + 2, the third term is 1 + 2 + 3 and so on.

**Square Numbers**

1, 4, 9, 16, 25, 36, …

The square numbers is a sequence of perfect squares: , , , , , , and so on.

**Cube Numbers**

1, 8, 27, 64, 125, …

Well, from square numbers, you surely have guessed what are cube numbers. They are a sequence of cube of integers.

, , , , …

**Fibonacci Sequence**

1, 1, 2, 3, 5, 8, 13, 21, …

Technically, a Fibonacci sequence is a sequence that starts with (0, 1), or (1, 1), and each term is the sum of the previous two. For example, in the sequence above, 5 is the sum of 2 and 3, while 21 is the sum of 8 and 13. In the actual examination, they may give Fibonacci-like sequences (technically called Lucas Sequence) where they start with two different numbers. For example, a Lucas sequence that starts with 1 and 3 will generate

1, 3, 4, 7, 11, 18, …

Of course, they can also combine positive and negative numbers to create such sequences. For example, a Lucas sequence that starts with -8 and 3 will generate the sequence

-8, 3, -5, -2, -7, -9, …

Well, this looks like a difficult sequence, but remember that if you can see the pattern, it is easy to look for the next terms.

*Images Credit: Math World*

If your internet is fast, you might want to watch our tutorial series on patterns and sequences. These videos are in Filipino.