This **question aims** to find the **next number** in the series of the **given numbers**. **Number series** is a **sequential arrangement of numbers** following a certain defined **pattern. **

** **

**Different types of number series**

The most **common pattern** in the **number series** are the following:

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**Series consisting of perfect squares**

A **series based on perfect squares** is mostly based on perfect squares of numbers in a **certain order**, and generally, one of the numbers in this type of series is missing.

**Example:** $4, 9, 16, 25,?$

**Sol:** $4 = 2^{2}, 9 = 3^{2}, 16 = 4^{2}, 25 = 5^{2}, 36 = 6^{2}$

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**Perfect cubes series**

It is **based on a number** **of dice in a certain order**, and one of the numbers in the row is missing.

**Example:** $27, 125, 343,?$

**Sol:** $3^{3}, 5^{3}, 7^{3}, 9^{3}$

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**Geometric series**

Geometric series is **based on either descending or ascending order of the numbers** and each subsequent number is obtained by **dividing** or **multiplying** previous number by a **specific number**.

**Example:** $4, 36, 324, 2916?$

**Sol:** $4 \times 9 = 36, 36 \times 9 = 324, 324 \times 9 = 2916, 2916 \times 9 = 26244$.

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**Arithmetic series**

It consists of a **series** in which next term is obtained by **adding/subtracting** a **constant number** from the** previous term**. **Example:** $-3,4,11,18$ where the number to be added to get the new number is $5$.

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**Two-stage type series**

In a **two-step arithmetic series**, differences of** consecutive numbers** form an arithmetic series.

**Example:** $2, 4, 7, 11..$

**Sol:** $4 – 2 = 2, 7 – 4 = 3, 11 – 7 = 4$

Now, the arithmetic sequence $2, 3, 4$

So $5$ is added to the** last number** given, so the answer is $11 + 5 = 16$

**Expert Answer**

The **next number** in the series is $20$.

Given series is $38,36,30,28,22$.

Seeing **alternative numbers**, there are** two** series.

**First series** is $38,30,22$.

The common difference between the** two consecutive numbers** is:

\[30-38=22-30=-8\]

**Second series** is $36,28$.

The **common difference** between the two consecutive numbers is:

\[28-36=-8\]

Therefore, the **next number** is

\[28-8=20\]

The **next number** is $20$.

**Numerical Result**

**The next number in the series** of the numbers $38,36,30,28,22$ is $20$.

**Example**

**What is next number in the series $1,4,9,16,25$?**

**Solution**

Given series is $1,4,9,16,25$.

**First number**: $1=1^{2}$

**Second number**: $4=2^{2}$

**Third number:** $9=3^{2}$

**Forth number:** $16=4^{2}$

**Fifth number:** $25=5^{2}$

The **series of the numbers** is $1,2,3,4,5$. The **next number** is $6$.

Therefore,

The** next number** is $6^{2}=36$.

**The complete series is $1,4,9,16,25,36$.**