Arithmetic Series and Sequences

Arithmetic sequence: \( A_n = A_1 + (n-1)d \)

Sum of first n terms: \( S_n = \dfrac{n}{2}(A_1 + A_n) = \dfrac{n}{2}\left[2A_1 + (n-1)d\right] \)

Two‑term derivation: \( d = \dfrac{A_p - A_k}{p - k} \quad;\quad A_1 = A_p - (p-1)d \)