Advances in International Applied Mathematics

Calculating the sum of the first n terms of sequences in high school mathematics is a common and key topic in the National College Entrance Examination (Gaokao), typically categorized as moderately challenging. It primarily assesses students logical reasoning and mathematical operation skills. By analyzing past Gaokao mathematics questions, this paper systematically elaborates on six solution strategies for sequence summation: direct application of the general term formula, the method of subtraction by dislocation (telescoping series), term-splitting and cancellation method, group summation method, reverse-order addition method, and derivation of the general term formula method. The study aims to provide practical references for teaching and exam preparation in sequence learning.

Sum of the first n terms of a sequence; Method of dislocated subtraction; Method of telescoping series; Group summation method