Summary
1. An arithmetic progression (AP) is a list of numbers in which each term is obtained by adding
a fixed number $d$ to the preceding term, except the first term. The fixed number $d$ is called the
common difference.
The general form of an AP is $a, a + d, a + 2d, a + 3d, . . . $
2. A given list of numbers $a_1,a_2,a_3......a_n$ is an AP,
if the differences $a_2-a_1$ ,$a_3-a_2$,... give the same value,
i.e., if $a_{k+1}-a_k$ is the same for different values of k.
3. In an AP with first term $a$ and common difference $d$, the nth term (or the general term)
is given by $a_n = a + (n – 1) d.$
4. The sum of the first n terms of an AP is given by :
$S_n$=$n/2$$[2a+(n-1)d]$
5. If $l$ is the last term of the finite AP, say the nth term, then the sum of all terms of the AP
is given by
$S$=$n/2$$[a+l]$
6.. If $a$, $b$, $c$ are in AP, then $b={a+c}/2$ and $b$ is called mean of $a$ and $c$.