A series of numbers or alphabets or both, seemingly unrelated in nature but having a certain underlying logic, gives us today’s topic. These type of questions are commonly seen in CET and are easy to moderate in nature. The number of questions can range from 10-20 and can be either found in a set of five questions or as a standalone question.

Series questions can be broadly divided into two types: the easily solvable and the apparently unsolvable types. With practice and exposure to various patterns, one can increase one’s range and add additional questions to the first category. As seen with many other topics, the expertise in this area can be vastly improved by getting to know the various patterns. There are a few things which one has to know so as to be able to spot the logic in any series question that one encounters.

What you need to know?

This is the list of things one should be well-versed with while solving the series questions:

1. Squares and square roots of at least the first 30 numbers.
2. Cubes and cube roots of the first 12 numbers at least.
3. Commonly used fractions and reciprocals of first 12 numbers at least.
4. The positions of letters in the alphabets, both forward and reverse.
5. All the prime numbers at least till 50.
6. Factorials of numbers from 1 through 7.
7. Formulae for calculating sum of squares, cubes and values of the same for the first few numbers.

While there are infinite possibilities of designing a series question, the commonly found patterns in CET are either of the three:

1. Gradually Increasing/Decreasing: There will be a gradual increase from the first to the last term of the series. The thing here would be to find if there is a pattern in the increase and then apply the same to the missing term.

In this type, it is advised to see the differences between the terms first and see if there is any pattern. The pattern might be a simple constant difference or an increasing or decreasing one. Sometimes, the difference can be a sum of two or more parts

For example:

5, 10, 23, 48, 99, ?

Here, if you observe the difference, it comes out to be 5, 13, 25, 41 and so on. Not really a pattern, is it? But, on careful observation, we can see that, the differences actually are nothing but sum of squares of consecutive integers (1^2 +2^2=5, 2^2+3^2=13 and so on).

5, 7, 19, 55, 135, ?

Here, the differences come out to be 2, 12, 36, 80 and so on. Again, seems to be a completely random pattern. But, on looking closer, one can see that the pattern is of the form (n^2+n^3 with the value of n increasing).

If one cannot get any pattern by finding the differences, one can check if there is any multiplication involved. For this, one needs to know simple reciprocals and some commonly used fractions.

?, 420, 360, 288, 192

Here, the difference comes out to be 60, 72, 96 and so on. So, apparently no logic involved. But, if we see the ratios of terms, 420/360=7/6, 360/288=5/4, 288/192=3/2. So, there is a pattern involved here.

Sometimes, there can be combinations of the two subtypes. This example was contributed by Vivek:

2, 11, 27, 113, 561, 3369

Here, it would be better if we took the larger terms first. We can find a relation between 561 and 3369 which is, 561*6+3=3369. Also, 113*5-4=561. So, we can see that the multiplier is getting gradually increased and the addition/subtraction element is decreasing. Also, the sign is alternating. These examples are complex in nature and are the differentiators between a serious aspirant and a casual one.

1. Alternating series: These are nothing but two series questions merged into one. As it involves thinking about two problems, it can be assumed that both the series are easy to comprehend. Once one is sure that there is no logic involved, one can go for checking for the alternating series questions. The two series can follow the same logic or two entirely different sets of logic.

The common questions here involve the alphabetical questions where in sets of three alphabets are given. In this, each letter is logically related to the corresponding letter of the next set. The logic can be any of the various ones we’ve covered.

1. Abstract series: There is no mathematical logic involved in few of the questions. There is some pattern which is to be discovered in such types.

1, 11, 21, 1211, 111221, ?

This is one series many might be aware of. Here, there is no mathematics involved. It just states the number which precedes itself. One, one one, two-ones, one-two one-one and so on.

Another one:

BC, EG, KM, QS

There isn’t a pattern here mathematically. The thing you can notice here is that, the letters used represent the prime numbers (2-3, 5-7, 11-13, 17-19).

Strategy:

Series questions are not that difficult to solve. They do take longer than say some of the other types like the calculative ones or the reasoning sets. But then, these questions bring with them sure-shot marks.

The questions can be either based on completing a series (either the end element or one of the intermediate elements) or spotting a wrong term in a given series. The latter one is more difficult to do as one cannot be sure if the set of numbers one is considering is the one with the error or not. In such a case, one can compare the adjacent numbers to see if there is any logic involved and then relate it to the next set of numbers.

The time taken to solve these questions entirely depends on how difficult the logic is which in turn depends on whether you have encountered such a pattern earlier. Once you know the logic, it only boils down to your calculation speed and the answer should be ready anywhere in 30-45 seconds. Knowing the things I’ve mentioned at the start will also help in solving other standalone logic questions. If one is unable to find the logic even after giving it a thought, one can leave the question and proceed to the next one. Also, there might be a mental block, which I had experienced many a time, wherein, if one cannot solve one of the questions, one finds it difficult to spot the logic in the next one. If this happens, one can take some time off the set of series questions and come back to it at a later stage.

Armed with these concepts, one should be able to tackle most of the series questions comfortably. The rest, well, it depends on the amount of hardwork you’ve put in.