Geometric Sequence - Example

The sequence $1, 2, 4, 8, 16, ...$ represents powers of $2$. This is a geometric sequence with $a_1 = 1$ and $r = 2$.

Using the formula $a_n = 1 \times 2^{n-1} = 2^{n-1}$, the 10th term is $a_{10} = 2^9 = 512$.

Geometric sequences with $r = 2$ appear in algorithm analysis (binary trees, divide-and-conquer), bit manipulation (binary representation), and exponential growth problems.