Mathematics · Grades 11–12
Sequences & series · Formula sheet
Rules, conditions and small examples in one printable reference.
Remember this
Arithmetic sequences
The first term is n = 1. Use one fewer step than the term number.
aₙ = a₁ + (n − 1)d
17 + (24 − 1) × 2 = 63
Sum of an arithmetic sequence
Pair the first and last terms; each pair has the same total.
Sₙ = n[2a₁ + (n − 1)d]/2
18 × (2 × 18 + (18 − 1) × 10) ÷ 2 = 1854
Geometric sequences
Multiply repeatedly by the common ratio; do not add it.
aₙ = a₁rⁿ⁻¹
12 × 4^(4 − 1) = 768
Finite geometric sums
Use n terms, starting with the first term a.
Sₙ = a(rⁿ − 1)/(r − 1), r ≠ 1
4 × (4^4 − 1) ÷ (4 − 1) = 340
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.