SL 1.3—Geometric sequences and series

A geometric sequence is multiplied by the same common ratio r at each step. With first term a, its nth term is uₙ = arⁿ⁻¹; a negative ratio alternates signs while a ratio between 0 and 1 produces decay in magnitude.

For 3, 6, 12, …, $a=3$ and $r=2$. The fifth term is $3\cdot2^4=48$ and the first five terms sum to $3(1-2^5)/(1-2)=93$. In a decay model with $0<r<1$, the same finite formula adds the first $n$ measured stages.

A sequence lists terms; a series sums them. This objective uses nth terms, finite sums and sigma notation, so do not replace $n-1$ by $n$ or import a sum-to-infinity formula from a neighbouring objective.