Other sequences
Find and check general terms using differences or sums.
Meaning
Even without a constant difference or ratio, a sequence may have structure in consecutive differences, partial sums, or groups of terms. An individual term can be recovered by subtracting consecutive partial sums. Sₙ contains all terms through aₙ, while Sₙ₋₁ contains the same terms except the last. Subtraction cancels the shared terms and leaves aₙ, explaining the difference of partial sums.
Example
Practice for this concept
Scope and references
Topics
Difference sequences, recovering terms from sums, rule-based sequences
Learning goal
Find and check general terms using differences or sums.
Helpful background
Compare differences and sums and connect them with algebraic simplification.
Other sequences
These ordinary choice questions provide limited practice in this concept. They do not establish independent solution, full-concept performance, or mastery.