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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. \(S_n= {a_1+a_n \over 2}.n={2a_1+(n-1)d \over 2}. n\)