Unit 1 Review: Sequences & Series

Arithmetic & geometric sequences/series • Growth & decay • Infinite geometric series

Arithmetic: \(t_n=a_1+(n-1)d\) Geometric: \(t_n=a_1 r^{\,n-1}\) Sums \(S_n\) Infinite Series \(S_\infty\) Growth/Decay \(A_n=A_0 r^n\)

What You Should Be Able To Do

Recognize and generate arithmetic and geometric sequences from rules, tables, or context.
Use \(t_n=a_1+(n-1)d\) and \(t_n=a_1 r^{n-1}\) to find specific terms and general terms.
Compute partial sums: \(S_n=\frac{n}{2}\big(2a_1+(n-1)d\big)\) and \(S_n=\frac{a_1(1-r^n)}{1-r}\) (\(r\neq1\)).
Decide when an infinite geometric series converges (\(|r|<1\)) and find \(S_\infty=\frac{a_1}{1-r}\).
Model growth/decay with \(A_n=A_0(1+p)^n\) and interpret percent increase/decrease.

I can classify a sequence as arithmetic/geometric and justify it. I can write a correct general term \(t_n\). I can compute partial sums \(S_n\). I can test convergence and compute \(S_\infty\) when \(|r|<1\). I can solve growth/decay problems with percent change. Progress autosaves to this device.