Sequence Differences Tool

Discover the differences between numbers in a sequence. And the differences between those differences and so on. You may discover the sequence's secrets.

images/seq-diff.js

How it Works

When we look at the differences between terms in a sequence, we can find hidden patterns!

Example 1: The sequence 3, 5, 7, 9, 11, ...

Let's find the differences between each consecutive number:

Sequence:	3		5		7		9		11
1st Difference:		+2		+2		+2		+2

The first differences are all 2 (constant). This tells us it is an arithmetic sequence (a linear relation like 2n + 1).

Example 2: The sequence 2, 5, 10, 17, 26, ...

Let's find the differences:

Sequence:	2		5		10		17		26
1st Difference:		+3		+5		+7		+9
2nd Difference:			+2		+2		+2

The first differences change, but the second differences (the differences of the differences) are all 2. This tells us the sequence is related to n² (a quadratic sequence).

Rule of Thumb:

If the 1st difference is constant, the rule is linear (like n)
If the 2nd difference is constant, the rule is quadratic (like n²)
If the 3rd difference is constant, the rule is cubic (like n³)