Geometric Sequences

Multiplying each time

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Geometric sequence: $a_n = ar^{n-1}$.
• Sum of the first $n$ terms: $S_n = a\frac{r^n - 1}{r - 1}$.
• Repeated doubling (or halving) gets huge (or tiny) astonishingly fast.

Steps

1. Fold to the Moon
2. Geometric sequences
3. Rice on a chessboard
4. Sum a geometric sequence
5. Adding up halves and more
6. Bouncing ball