# Number Series Rules with solved Problems - TNPSC Number Series

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 ?
• Perfect Cube
Example :
6859, 5832, 4913, 4096, 3375, ?
2. Difference Series
Example :
1348, 1338, 1318, 1288, 1248, ?
3. Ratio Series
Example :
336, 168, 84, 42, 21, ?
4. Mixed Series
Example :
222, 441, 1321, 2639, 7915, ?
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.