Arithmetic Vs Geometric

Arithmetic sequences add a fixed amount each step — 3, 7, 11, 15 — so they grow in a straight line. Their cousins, geometric sequences, multiply by a fixed factor — 3, 6, 12, 24 — so they explode.

Start at 3. Add 4 ten times and you reach 43. Double ten times instead and you reach 3,072.

Most real growth is geometric: compound interest, populations, a rumor spreading. Arithmetic growth shows up when something is held to a steady pace — fixed monthly payments, bus stops, page numbers. Mixing them up is costly. People expect savings to creep up arithmetically and are stunned when compounding takes off.