Look at what you can do now:
Recognize arithmetic sequences (constant difference) and geometric sequences (constant ratio)
Find the -th term using formulas: for arithmetic, for geometric
Use sigma notation to represent sums compactly
Apply closed-form formulas: , geometric series, arithmetic series
Recognize telescoping sums where intermediate terms cancel
Explain why nested loops take time using summation formulas
Sequences and summations are the foundation of algorithm analysis. Every time you count operations or optimize nested loops, you use these formulas. Good job. You're ready for the next section.