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# Mixed Series

The concept of mixed series is central to the number series in many exams. In a mixed series, more than one arithmetic operations are part of the rule according to which the series is formed. For example, a rule that has addition, subtraction and even one more operation as part of the rule that forms the series, is a mixed series. Here we will see some common examples of the mixed series and try to guess some rules. Let us begin!

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Let us see a few examples of mixed series. But first, let us list ourselves a few guidelines that will help us greatly to reduce the time consumption and improve the accuracy of our predictions. The following rules can be very helpful:

• Don’t spend much time on series questions. There will be only a few questions and if you are not able to find a rule in a minute, it is better to leave it and move on to the other questions. these questions usually take a long time if they are not identified at once.
• Classify the series that is present. Like if a number is followed by a number greater than it, then it is either multiplied by some factor or added by some factor. But this too doesn’t work in a mixed series as we shall see.
• Overall, the questions on series are entirely and solely dependent on the amount of familiarity that you have with these questions. In other words the more you have practised, the better it is. Source: Pinterest

As we will see in the following examples, the questions based on the mixed series could be very intimidating at times. But the trick here is to identify the series first. A geometric series increases steadily and so does an arithmetic series. But a mixed series may or may not present a regular pattern of increase or decrease. That is one way of detecting that a given series is a mixed series.

### Type I

The mixed series can be of many types. For example, here we shall see the wrong series kind first. Let us start with a few examples to introduce the concept of mixed number series.

In the following questions, a series of numbers are present. One of the numbers in the series doesn’t belong. Select the number that doesn’t belong.

Q 1: 10, 22, 69, 280, 480

A) 10       B) 22        C) 69          D) 280         E) 480

Answer: This is a mixed series as we shall see in a few moments. To detect the wrong number. we have to first detect the rule of the series. The rule could be the following:

9 1 + 1 = 10

10 2 + 2 = 22

22 3 + 3 = 69

69 4 + 4 = 280

280 5 + 5 = 1405

Thus not only do we have to detect the rule for the formation of the series but also compute the terms using the rule. The correct option here is thus E) 480 which is the wrong number and has to be replaced by 1405.

Questions like these could be a hassle and in such cases, if there is no apparent rule in one minute, you should move on to other questions and mark this one for future review.

### Type II

The next type in the mixed series is the series where there is a missing number. The missing number series questions, if any are usually from the mixed number series. A mixed series can be detected easily, through the fact that it lacks a regular symmetry. Basically, if you can’t figure out the rule easily, it is most probably a mixed series. Let us see a few missing numbers mixed series calculations.

In the following question, series of numbers has a missing term. The missing term is present below in the options. Select the correct number and complete the series.

Q 1: 1, 9/2, 28/3, 65/4, ___

A) 126/5         B) 95/5           C) 113/5              D) 15

Answer: This is an easier problem considering that there are a few hints here. the first hint is that each of the terms is divided by the term number. That is the second term is divided by the number ‘2’, the third by the number ‘3’, the fourth by the number ‘4’. So the fifth should have 5 in the denominator. But wait! What if the fifth number is a factor of 5? Then, in that case, the option will be simply D). But let us examine the series first.

The first term is 1 and gives no information. The second term is 9. The term number is 2. The question thus is how do you get a 9 from 2? Well (23 + 1) = 9 and thus the term could be written as (23 + 1)/2 = 9/2. The third term is (33 + 1)/3 = 28/3 and so on. Thus we have found the rule and the answer to the question is (53 + 1)/5 = 126/5.

## Practice Questions

Q 1: In the following series, a number is wrongly been inserted. Detect the number and select the correct option from the options that are given below:

22, 45, 72, 90, 130

A) 22.        B) 45.       C) 72.       D) 90.

Ans: B) 45 [Correct number is 46]

Q 2: In the following series, a number is missing. Find the missing number and select the correct option that has been put below:

1, 1/4, 1/9, 1/16 __

A) 1/32        B) 1/64          C) 1/25        D) 1/28

Ans: C) 1/25

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