Finding the Next Two Terms of a Sequence Using the Method of Differences

① This example demonstrates how to use the method of differences (successive subtraction) to find the next two terms of a sequence, with interactive input for verification. ② The core mathematical concept is finite differences: by examining first, second, or higher-order differences, one can extrapolate the pattern to predict future terms. ③ Construction details: GeoGebra commands include RandomElement and Random to generate random sequences, Sequence to build difference lists, Textfield and InputBox for user input, If to check correctness, and button1 to generate a new sequence. Key objects are lists l1, l2, l3, sequence terms u_1 through u_7, and text objects text1-text4 for instructions and feedback. ④ This is suitable for middle or high school students learning sequences, as well as for math competition preparation, providing a hands-on way to understand and verify the difference method.