Number Series Rules with solved Problems

Series is an important chapter from banking examination point of view. Following are some of the important rules or order on which the number series can be made :-

1. Pure Series
2. Difference Series 
3. Ratio Series 
4. Mixed Series
5. Geometric Series
6. Two Tier Arithmetic Series
7. Other Type

1. Pure Series

In this type of number series, the number itself obeys certain order so that the character of the series can be found out.

The number itself may be.

• Perfect Square 

Example :

121, 144, 169, 225 ?

Answer - 256

• Perfect Cube

Example :

6859, 5832, 4913, 4096, 3375, ?

Answer - 2744 

2. Difference Series

Example :

1348, 1338, 1318, 1288, 1248, ?

Answer - 1198

3. Ratio Series

Example :

336, 168, 84, 42, 21, ?

Answer - 10.5

4. Mixed Series

Example : 

222, 441, 1321, 2639, 7915, ?

Answer - 15827

5. Geometric Series

Example 1. 5, 35, 245, 1715, ?

Ans. 12005

Examples 2. 43923,3993, 363, 33, ?

Ans. 3

6. Two-tier Arithmetic Series

7. Other Type

To find the odd number from the number series. In this type of series the above rules are also followed.

Some Examples ;

•  2, 3, 7, 22, 89, 440, 2677, 18740

Solution : ×1+1, ×2+1, ×3+1, ×4+1, ×5+1 ........

 So, 440 is replaced by 446

• 5, 6, 14, 40, 89, 170, 291

Solution : +1², +3², +5², +7², +9²

 So, 14 is replaced by 15.

• 445, 221, 109, 46, 25, 114, 4

Solution : -3÷2, -3÷2........
So,46 is replaced by 53.

• 12, 26, 56, 116, 244, 498, 1008

Solution : ×2+2, ×2+4 ×2+6,  ........

So, 116 is replaced by 118

• 8, 27, 64, 125, 217, 343

Solution : 2³, 3³, 4³, 5³,.....

So, 217 is replaced by 216

Three Steps to Solve A Problem on Series

Step 1. Determine whether the series is increasing, decreasing or alternating.

Step 2. If the series is increasing or decreasing, then check :

1. if change is slow or gradual, then it is a difference series
2. if the change is equally sharp, throughout, then it is a ratio series.
3. if the rise is very sharp initially , but slows down later, then series may be formed by adding squared or cubed numbers

If the series is alternating or irregular , there may be either a mix of two series or two different kinds of operations going on alternately.

Step 3. Complete the series accordingly.

I have made a video tutorial for this chapter here.