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_1b_1, a_2b_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 = (a+c)/2 (arithmetic mean). If four numbers a, b, c, d are in AP, then a+d = b+c.