For summing products of consecutive terms of an AP: T_r = a_r * a_{r+1} * ... * a_{r+p-1}. Define V_r = a_r * a_{r+1} * ... * a_{r+p}. Then V_{r+1} - V_r = (p+1)dT_r (where d is common difference). So sum(T_r) = [V_{n+1} - V_1]/[(p+1)*d]. Example: sum(r(r+1)) = [r(r+1)(r+2)/3] evaluated at boundaries.