Easy Practice — Set 2

Quick Recap — Geometric Progressions

• $n$th term: $a_n=ar^{n-1}$; sum: $S_n=\dfrac{a(r^n-1)}{r-1}$ ($r\ne1$).
• Infinite sum (for $|r|<1$): $S_\infty=\dfrac{a}{1-r}$.
• Geometric mean of $a,b$ is $\sqrt{ab}$; $a,b,c$ in GP $\iff b^2=ac$.
• Consecutive terms have a constant ratio $r$.