Question

(fill in the blank) an-an-1=_________​

Answer 1

$a_n$ is the 'n'th number in the series.

The answer might be $\sf{a_n-a_{n-1}=d\:(n\geq 2)}$ because this question is mostly asked in the arithmetic progression.

But take a note that $\sf{a_n-a_{n-1}}$ could be another series, if more information is given.

More information:

The difference sequence(progression) is a special case where $\sf{a_n-a_{n-1}}$ is an independent series(A.P).

Here is an example: 1, 2, 4, 7, 11, ..., until $\sf{\dfrac{n^2-n+2}{2} }$.

Difference is 1, 2, 3, 4, 5, ..., until n-1

The difference between any two terms is an arithmetic series.