A Teaser on Answering Number Series Questions

First of all, I would like to point out the term series in the “Number Series” questions in the Civil Service Examinations is a bit incorrect. Technically, the list of numbers in the examinations is actually called a sequence.  A series is a sequence of sums — well, I will not go into details since it is not included in the examinations.  You can  click the link though if you want to know about it.

Second, this is quite a premature discussion since I have only written a few posts about integers. I planned to write about this later, but I thought that a teaser would be nice. In this post, I will show you that it is a must to master all the topics in mathematics because they are all connected. We will not discuss the strategies on how to answer the sequence problems here; I will have a separate post about them later. Don’t stop reading though because you are going to miss half of your life if you do (kidding).

A sequence or a progression is an ordered list of objects which can be numbers, letters, or symbols.  The list 3, 7, 11, 15, 19 is a sequence where 3 is the first term and 19 is the fifth term. Of course, it is easy to see the sixth term is 23 since each term is the sum of 4 and term before it.

There are also sequences that are in decreasing order such as 12, 5, -2, -9, -16 and so on. As you can observe, to get the next term, 7 is subtracted from the term before it. Notice also that this sequence needs knowledge on subtraction of negative integers.

The list

\displaystyle \frac{3}{5}, \frac{11}{10}, \frac{8}{5}, \frac{21}{10}, \frac{13}{5}

is also an example of a sequence. This sequence involves addition of fractions. The next term can be easily solved by converting the given into similar fractions which when done will result to

\displaystyle \frac{6}{10}, \frac{11}{10}, \frac{16}{10}, \frac{21}{10}, \frac{26}{10}.

Clearly, we only need to add \frac{5}{10} to the last term to get the next term which equals \frac{31}{10}.

In the sequences above, we have only used two number representations (integers and fractions) and two operations (addition and subtraction). In the actual Civil Service Examinations, the sequences can also include one or a mixture of other number representations such as percent, decimal, mixed numbers, and a combination of these representations. They can also include the four fundamental operations (addition, subtraction multiplication and division). When I took the Civil Service Examination in 2002 and 2003, there are fractions, whole numbers, and decimals in a single given number sequence.  I know that 2002 was a long time ago, but the format of the examination had not changed since.

For now, we will abandon sequences and return to basic Mathematics and English in the next few posts. When all the pre-requisite knowledge are discussed, we will learn the strategies on answering number sequence questions.

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