Solving Number Series Type 2 - Verbal Reasoning Problems

Some common types of number series reasoning problems are:
1. Series with a constant difference
2. Series with an increasing difference
3. Series with a decreasing difference
4. Squares/ Cubes series
5. Combination of different operations
6. Miscellaneous

1. Series with a constant difference
In this kind of series, any 2 consecutive numbers have the same difference between them.

For example: 1 , 5 , 9 , 13 , ?

We can observe that we are adding 4 to the previous number to obtain the next number. So, answer here will be 13+4 = 17.

2. Series with an increasing difference
In this type of series, the difference between two consecutive terms keep on increasing as we move forward in a series. Let us try to use this theory in a question.

1,2,4,7,11,16,?

We can clearly observe that the series is increasing with the difference : +1, +2, +3 ,+4 , +5.

So, we will obtain our number by adding 6 to 16 which gives us 22.

3. Series with a decreasing difference
In this type of series, the difference between two consecutive terms keep on decreasing as we move forward in a series. Let us try to use this with some modification in the previous question that we did.

For example: 16,11,7,4,2, ?

We can clearly observe that the series is decreasing with the difference : -5, -4, -3 ,-2 .

So, we will obtain our number by subtracting 1 from 2 which gives us 1.

4. Squares/ Cubes series
We can have series where the terms are related to the squares/ cubes of numbers. We can have a lot of variations here. Let us look at some of the possibilities.

1, 9, 25, 49 , ?

We can observe that the above series is square of odd numbers starting from one. So our answer will be 9^2 = 81.

For example: 1 , 1 , 2 , 4 , 3 , 9 , 4 , ?

We observe here that the series is formed by writing numbers starting from 1 along with its square as the next number i.e. ( 1 , 12) , (2, 22) and so on. So we obtain our answer as 16 which is 42.

For example: 9 , 28 , ? , 126.

The answer for above question will be 65, let us see how.

9 , 28 , ? , 126.

( 23+1) (33+1) (53+1)

The blank should have 43+1. Hence, the answer is 65.

5. Combination of different operations
This kind of series has more than 1 type of arithmetic operations which have been performed or it can also have 2 different series which have been combined to form a single series. This kind of series is the the most asked and the most important among all the types of series that we have discussed so far.

For example: 1, 3 , 6 , 2 , 6 , 9 , 3 , 9 , ?

The first term 1 is multiplied by 3 to give the second term, 3 has been added to the second term to get the third term. The next term is 2 which is 1 more than the 1st term. It is multiplied with 3 to give next term and the process is continued. With this process, we obtain our answer as 12.

For example: 6, 10 , 7, 11 , 8 , 12 , ?

We can see that the above series is a combination of 2 simple series:

1st , 3rd , 5th terms make an increasing series of 6 , 7 , 8….. . The 2nd , 4th and 7th term make a series of 10 , 11 , 12… . So, our answer will be 9 which is the 7th term of the original series.

6. Miscellaneous series
Some series do not come under any of the above mentioned categories but are very important and also asked in many examinations.

The series of prime numbers or any other related operation done on it comes under this category.

For example: 9, 25 , 49 , 121 , ?

The above series is the squares of prime numbers. So next term will be square of 13 which is 169.

Now let’s starts the detail discussion of Number Series Questions Type 2 and few important reasoning questions and answers.

Example 1
What would be the missing term replaces in the question mark?

1, 9, 25, 49, 81, ?
Solution:

Each term is increases sequentially square

1², 3², 5², 7², 9², 11².

So, missing term is 11² = 121.
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Example 2
What would be the missing term replaces in the question mark?

1, 7, 15, 25, 37, ?
Solution:

Each term obtain with +6, +8, +10, +12, +14...onward.

So, missing term is 37 + 14 = 51.
 
 
Example 3
What would be the missing term replaces in the question mark?

0, 2, 6, 12, 20, ?
Solution:

Each term obtain 1²– 1 = 0, 2²– 2 = 2, 3²– 3 = 6...onward.

So, missing term is 6²– 6 = 30
 
 
Example 4
What would be the missing term replaces in the question mark?

13, 17, 25, 41, 73, ?
Solution:

Each term obtain with +2², +2³,+2⁴,+2⁵…. onward.

So, missing term is+2⁶ = 137.
 
 
Example 5
What would be the missing term replaces in the question mark?

6, 18, 38, ? , 102
Solution:

Each term obtain with +2²+ 2 = 6, +4²+ 2 = 18, +6²+ 2...nward.

So, missing term is 8²+2 = 66.
 
 
Example 6
What would be the missing term replaces in the question mark?

2, 24, 68, 134, 222, ?
Solution:

Each term obtain with +( 11 x 2 ), +( 11 x 4 ),+( 11 x 6 ), +( 11 x 8 )...onward.

So, missing term is 332.
 
 
Example 7
What would be the missing term replaces in the question mark?

5, 20, 45, 80, ?
Solution:

Each term obtain with 5 x 1², 5 x 2², 5 x 3²...onward.

So, missing term is 125.
 
 
Example 8
What would be the missing term replaces in the question mark?

7, 25, 61, 121, 211, ?
Solution:

Each term obtain with 2³ -1, 3³ – 2, 4³ – 3...onward.

So, missing term is 337.
 
 
Example 9
What would be the missing term replaces in the question mark?

1, 3, 2, 6, 5, 15, ?
Solution:

Each term obtain with x3, -1, x3, -1...onward.

So, missing term is 14.
 
 
Example 10
What would be the missing term replaces in the question mark?

36, ? , 64, 81, 100, 121
Solution:

Each term obtain with 6², 7², 8², 9²...onward

So, missing term is 7² = 49