1Question 1
Given $a_1 = 12$ and $r = 0.5$, compute $a_8$.
2Question 2
A sequence begins $5, 10, 20, 40, \dots$. (a) Find the common ratio. (b) Write a formula for $a_n$. (c) Determine $a_9$.
3Question 3
If $a_3 = 45$ and $a_6 = 1,215$, determine $a_1$ and $r$.
4Question 4
A bacteria culture triples every $4$ hours. If $a_1 = 800$ cells at hour $0$, how many cells are present after $16$ hours?
5Question 5
Compute $S_6$ for the geometric sequence with $a_1 = 4$ and $r = -1.5$.
6Question 6
Decide whether the sequence $-81, 27, -9, 3, \dots$ is geometric. If so, state $r$ and $a_n$.
7Question 7
A savings challenge deposits $a_n = 300(1.08)^{n-1}$ rand each week. Find the smallest $n$ for which $a_n ge 800$.
8Question 8
How many terms are required so that a sequence with $a_1 = 5$ and $r = 2$ has $S_n = 635$?
9Question 9
A medicine decays by $12\%$ every hour from an initial $180\,\text{mg}$. After how many hours will the dose drop below $50\,\text{mg}$?
10Question 10
For $a_n = 162\left(\frac{1}{3}\right)^{n-1}$, determine $a_7$ and $S_6$.