# How to Solve IQ Sequences, Series & Number Pattern Problems in IQ Tests?

Posted BY Admin

Posted Date  29/06/2019

In general, there are 2 types of IQ series & pattern problems we have to face while appearing in IQ Tests.

1. Number Series & Sequences

2. Alphabetical Series & Sequences

Below both types of problems and their solutions are discussed one by one in detail.

1. Number Series, Sequences & Patterns

In these types of problems, a sequence of numbers is given to you and ask last, middle or first term of the sequence.

For example

What comes next?

2, 4, 6, 8, 10, … ?

Here I took the simplest example, some numbers are given and the next expected number is being asked. You need to find out the relationship between the known terms first, then need to apply the same relationship to the next terms finally reaching the unknown term. Here in this example, we can see that each term is retrieved by adding “2” in the previous term. like

2 + 2 = 4

4 + 2 = 6

6 + 2 = 8

8 + 2 = 10

So

10 + 2 = 12 (Answer)

In number series, 3 types of sequences can be found

Arithmetic Series (a common difference exists between terms, same as in the example)

OR

Geometric Series (a common ratio exists between terms)

OR

Neither.

In most of the IQ Tests, Arithmetic series questions are common, you can follow the steps below to find the next term

If Arithmetic Series

• Find the common difference.

Remember, subtract from a particular term, the term that immediately precedes it.

For example

What comes next in the sequence 5, 10, 15, 20,…?

subtract 5 from 10 or 10 from 15, etc. Here, the common difference is 5. Hence next term of the sequence is 25. Now as we found the exact logic we can find the next “n” terms of the sequence.

If the sequence terms are decreasing from left to right, the common difference should be negative.

For example

1000, 950, 900, 850, …?

Here the common difference is -50 and the next term is 800.

• Multiply the common difference to “n", the term number. In the sequence above in step 1,  you should have 5n as one part of the general term.

If Geometric Series

• Find the common ratio, more specifically the ratio between a particular term and the term that immediately precedes it.

For example

What comes next in the sequence 10, 50, 250, 1250,…?

Divide 50 by 10 or 250 by 50 and 1250 by 250. You should get 5.

Your common ratio is 5.

Hence next term of the sequence is

1250 x 5 = 6250.

If the sequence features decreasing numbers as terms but still have a common ratio, then the common ratio should be a fraction between 0 and 1 (or increasing but the terms are negative, the ratio should be a fraction between 0 and -1).

If Neither Arithmetic Nor Geometric Series

We also have to face some other types of series which are neither Arithmetic nor Geometric, rather we have to solve them logically. We need to find the relationship between known terms to reach the unknown terms.

Examples

• 2, 3, 5, 7, 11, 13, …?

This sequence contains the prime numbers. So the next prime number 17 is the next term.

In this example there are 2 series 100, 97.5, 92.5, 85, … And 1, 3.5, 8.5, 16, … In First series 2.5, 5, 7.5 & 10, … are subtracted from each terms so next number is 85 - 10 = 75. In Second series same numbers are being added started from 1. So next terms is 16 + 10 = 26. Hence next 2 terms of main sequence are 75, 26.

In this example Add 2, 6, 18, 54, … in each term. Here

6 = 2 x 3

18 = 6 x 3

54 = 18 x 3

So 35 + 54 = 89 is answer.

You can find many other logical Numbers Series & Patterns problems with solutions here.

2. Alphabetical Series, Sequences & Patterns

Alphabetical series is also the same as number series. But the only difference is that we have to deal with alphabets as compare to numbers. It can also be an arithmetic or geometric series, or neither. The easiest way to solve alphabetical series is to convert all alphabets in digits starting from 1. Like “a” should be assigned as 1, “b” as 2 and “z” as 26. After converting to digits, we surely find a pattern between numbers which lead us to find the next missing number. Finally converting back that number to the alphabet gives us the missing term of the sequence.

Examples

• A, C, E, G,…?

If we write this series into number series like 1, 3, 5, 7, …? We can easily guess that 1 number is skipped (its a sequence of odd numbers). In our original alphabetical series by skipping 1 alphabet after “G”, we get “I”. which is the answer.

This is a reverse alphabetical series. Skip 2 and 3 alphabets alternatively in reverse order to find the next missing alphabet, which is “C”.

These are 2 parallel series, one with skipping 2 alphabets in reverse order A, X, U, R, … and other with skipping 2 alphabets in forwarding order E, H, K, … Hence next term of the sequence is “K”.

In this example, alphabets are missed in the order 0, 1, 2, … So the next term of the sequence is “U” by skipping 4 alphabets after “P”.

These are the common IQ related series & sequences problems we have to face in IQ Tests. You can find many other similar logical problems with solutions here. If you are really interested to increase your IQ must read my blog “5 Easiest Ways to Improve IQ Level”. I hope it will also help you a lot in your IQ Test Preparation & Tests.

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