Property 1: In a finite AP, the sum of terms equidistant from the beginning and end is constant: $a_1$ + $a_n$ = $a_2$ + $a_{n-1}$ = ... = a + l.

Property 2: If $a_1$, $a_2$, ..., $a_n$ is AP, then $a_{1+k}$, $a_{2+k}$, ..., $a_{n+k}$ is also AP (shifting). And $ca_1$, $ca_2$, ..., $ca_n$ is AP (scaling).

Property 3: If $a_1$, ..., $a_n$ and $b_1$, ..., $b_n$ are both AP, then a_{1+b}_1, a_{2+b}_2, ... is AP. But $a_1$$b_1$, $a_2$$b_2$, ... is generally NOT AP.

Property 4: If $S_n$ of an AP is given, then $a_n$ = $S_n$ - $S_{n-1}$ (for n >= 2) and $a_1$ = $S_1$.

Property 5: The nth term from the end of an AP = l - (n-1)d where l is the last term.

Property 6: If three numbers a, b, c are in AP, then b = $\frac{a+c}{2}$ (arithmetic mean). If four numbers a, b, c, d are in AP, then a+d = b+c.