The difference series can be further classified as follows. .

(a) Number series with a constant difference. .

(b) Number series with an increasing or decreasing difference. .

In
the number series with a **constant difference**, there is always a constant
difference between two consecutive numbers.

For example, the numbers of the series 1, 4, 7, 10, 13, ... . . are such that any number is obtained by adding a constant figure of 3 to the preceding term of the series.

If we have to find the next number in the above series, we need to add a 3 to the last term 13. Thus, 16 is the next term of the series.

Under the series with constant difference, we can have series of odd numbers or series of even numbers also. .

In
the series with **increasing/decreasing difference**, the difference between
consecutive terms keeps increasing (or decreasing, as the case may be). For
example, let us try to find out the next number in the series 2, 3, 5, 8, 12,
17,23, ...

Here, the difference between the first two terms of the series is 1; the difference between the second and third terms is 2; the difference between the third and the fourth terms is 3 and so on. That is, the difference between any pair of consecutive terms is one more than the difference between the first number of this pair and the number immediately preceding this number. Here, since the difference between 17 and 23 is 6, the next difference should be 7. So, the number that comes after 23 should be (23 + 7) = 30. .

We can also have a number series where the difference is in decreasing order (unlike in the previous example where the difference is increasing). For example, let us find out the next term of the series 10, 15, 19, 22, 24,..... .

10, 15, 19, 22, 24

+5 +4 +3 +2

Here the differences between1^{st }& 2^{nd},
2^{nd} & 3^{rd}, 3^{rd} & 4^{th}
numbers, etc. are 5, 4, 3, 2, and so on. Since the difference between 22 and 24
is 2, the next difference should be 1. So, the number that comes after 24
should be 25. .