# Series - Arithmetic series

Initial term : $a_1$
$N^{th}$ term : $a_n$
Difference between successive terms : d
Number of terms in the series : n
Sum of the first n terms : $S_n$

1. $a_n= a_{n-1}+d=a_{n-2}+2d=...=a_1+(n-1)d$
2. $a_1+a_n=a_2+a_{n-1}=...=a_i+a_{n+1-i}$
3. $a_i={a_{i-1}+a_{i+1} \over 2}$
4. $S_n= {a_1+a_n \over 2}.n={2a_1+(n-1)d \over 2}. n$