 # The next number in the series 38, 36, 30, 28, 22 is ? 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:

• 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. Perfect square

Example: $4, 9, 16, 25,?$

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

• 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: $3^{3}, 5^{3}, 7^{3}, 9^{3}$

• 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. Geometric series

Example: $4, 36, 324, 2916?$

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

• 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 $5$. Sum of arithmetic series

• 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 $11 + 5 = 16$

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 $1,4,9,16,25,36$.