Mathematics · Grades 10–12
Geometric sequences
Multiply repeatedly by the common ratio; do not add it.
The key idea
Multiply repeatedly by the common ratio; do not add it.
aₙ = a₁rⁿ⁻¹
Worked examples
A geometric sequence starts at 12, with common ratio 4. Find term 4.
12 × 4^(4 − 1) = 768
768
A geometric sequence starts at 10, with common ratio 3. Find term 7.
10 × 3^(7 − 1) = 7290
7290
Try it yourself
A geometric sequence starts at 9, with common ratio 2. Find term 5.
A geometric sequence starts at 7, with common ratio 2. Find term 4.
Check your understanding
Answers and marking notes
- 144
9 × 2^(5 − 1) = 144
- 56
7 × 2^(4 − 1) = 56
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.