PEAZIT Aha card
Go straight to resources ↓Geometric sequences: multiply by the same factor
To reach the nth term from the first, multiply by q exactly n − 1 times: a_n = a_1 · q^(n − 1). q is the common ratio.
| Expression | Meaning |
|---|---|
| a_1 = 3; q = 2 | The ratio of neighbouring terms is 2. |
| a_5 = 3 × 2^4 | Four multiplications lead from first to fifth. |
| a_5 = 48 | 3 × 16 = 48. |
One worked example
- a_1 = 3; q = 2The ratio of neighbouring terms is 2.
- a_5 = 3 × 2^4Four multiplications lead from first to fifth.
- a_5 = 483 × 16 = 48.
Watch out: The ratio may be fractional or negative. When finding q by division, the preceding term must be nonzero.
Goal, prerequisites and card origin
What you will learn: Find the nth term of a sequence with a constant multiplier.
What you need first: Powers and multiplication.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
To reach the nth term from the first, multiply by q exactly n − 1 times: a_n = a_1 · q^(n − 1). q is the common ratio.