Grade 12 · Theory
Geometric sequences
Sequences and series · about 3 min
Visual overview: Geometric sequences1 MIN READ
2 study sections · pause after each one and recall the key ideaA geometric sequence multiplies by a constant ratio, producing rapid growth or decay.
Key points- General term: Tₙ = a·r^(n−1), where r is the constant ratio.
- r = T₂/T₁ = T₃/T₂.
- Sum of n terms: Sₙ = a(rⁿ − 1)/(r − 1) for r ≠ 1.
- Alternate signs mean r is negative.
- Common ratio (r) — the constant multiplier.
EXAM TIP
to prove a sequence is geometric, show the RATIO between consecutive terms is constant — not the difference.