Section Recap

Look at what you can do now:

$1.$ Recognize arithmetic sequences (constant difference) and geometric sequences (constant ratio)

$2.$ Find the $n$-th term using formulas: $a_n = a_1 + (n-1)d$ for arithmetic, $a_n = a_1 \times r^{n-1}$ for geometric

$3.$ Use sigma notation to represent sums compactly

$4.$ Apply closed-form formulas: $\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$, geometric series, arithmetic series

$5.$ Recognize telescoping sums where intermediate terms cancel

$6.$ Explain why nested loops take $O(n^2)$ 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.