Types of Number Series:

There are different types of number series, which are as follows:

1. Arithmetic Series: In an arithmetic series, the difference between consecutive terms is constant. For example, 2, 5, 8, 11, 14 is an arithmetic series with a common difference of 3.

2. Geometric Series: In a geometric series, each term is multiplied by a constant factor to obtain the next term. For example, 2, 6, 18, 54, 162 is a geometric series with a common ratio of 3.

3. Fibonacci Series: In a Fibonacci series, each term is the sum of the two preceding terms. For example, 1, 1, 2, 3, 5, 8, 13, 21, 34 is a Fibonacci series.

4. Square Series: In a square series, each term is the square of a number. For example, 1, 4, 9, 16, 25 is a square series.

5. Cube Series: In a cube series, each term is the cube of a number. For example, 1, 8, 27, 64, 125 is a cube series.

6. Prime Number Series: In a prime number series, each term is a prime number. For example, 2, 3, 5, 7, 11, 13, 17, 19, 23 is a prime number series.

7. Odd/Even Series: In an odd/even series, each term is either an odd or an even number. For example, 2, 5, 8, 11, 14 is an even series, and 1, 3, 5, 7, 9 is an odd series.

8. Mixed Series: In a mixed series, different types of number series are combined. For example, 1, 4, 9, 28, 35, 46, 67, 82 is a mixed series.

Conclusion:

Therefore, it is important to identify the type of number series to predict the next number accurately. In the given series 4,6,9,14,21, it is not possible to accurately predict the next number without knowing the type of series. However, it is possible that the next number could be 30, as the difference between consecutive terms is an odd number.