**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 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 :**+1

^{2}, +3

^{2}, +5

^{2}, +7

^{2}, +9

^{2}

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 :**2

^{3}, 3

^{3}, 4

^{3}, 5

^{3},.....

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 :

- if change is slow or gradual, then it is a difference
series
- if the change is equally sharp, throughout, then it is
a ratio series.
- 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.

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