**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 :-

*Pure Series*

*Difference Series*

*Ratio Series*

*Mixed Series*

*Geometric Series*

*Two Tier Arithmetic Series*

*Other Types*

**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